Axioms

15 pages, 284 KB

Open AccessFeature PaperArticle

Laplace Convolution Integrals Involving Trigonometric and Hyperbolic Functions

by Juan Luis González-Santander

Axioms 2026, 15(6), 416; https://doi.org/10.3390/axioms15060416 - 3 Jun 2026

We calculate several finite integrals involving trigonometric and hyperbolic functions by applying the Laplace convolution theorem and known inverse Laplace transform formulas. As a consequence, we obtain a new integral representation of the Kelvin function

bei (z)

, and a new [...] Read more.

We calculate several finite integrals involving trigonometric and hyperbolic functions by applying the Laplace convolution theorem and known inverse Laplace transform formulas. As a consequence, we obtain a new integral representation of the Kelvin function

bei (z)

, and a new reduction formula for a particular generalized hypergeometric function. In addition, we present several new inverse Laplace transform formulas that do not appear to have been reported in the existing literature. Full article

(This article belongs to the Special Issue Recent Advances in Special Functions and Applications, 2nd Edition)

15 pages, 1135 KB

Open AccessArticle

Graph-Structured Persistent Memory for Efficient LLM-Based Computer Use Agents

by Danylo Vorvul, Andrii Musienko, Iryna Galchenko, Mykola Myroniuk and Andrii Sobchuk

Axioms 2026, 15(6), 415; https://doi.org/10.3390/axioms15060415 - 2 Jun 2026

Abstract

Large language model (LLM)-driven computer use agents (CUAs) automate graphical user interface (GUI) tasks but often re-solve previously encountered subtasks, increasing token use and latency. We address this limitation with a directed graph-based persistent memory in which nodes represent observable GUI states and [...] Read more.

Large language model (LLM)-driven computer use agents (CUAs) automate graphical user interface (GUI) tasks but often re-solve previously encountered subtasks, increasing token use and latency. We address this limitation with a directed graph-based persistent memory in which nodes represent observable GUI states and edges encode executable action sequences. We formalize the memory-augmented agent as

S = ⟨ A, Σ, G, δ, π, Φ ⟩

, define task reachability and memory-coverage conditions inspired by functional stability theory, and derive token-cost efficiency bounds. In control-theoretic terms, the Manager–Worker architecture can be interpreted as a closed-loop system where memory provides experience-based feedback; this interpretation is used as an analogy rather than a full model-reference adaptive control proof. Experiments on OSWorld show that the proposed agent cuts both the LLM token consumption and execution time by about 50% versus a memoryless baseline while preserving comparable success rates (≈36.9% on 15-step and ≈46.9% on 50-step tasks). The demonstrated contribution is therefore operational efficiency through reusable graph memory, not a claim of improved task success or classical Lyapunov stability. Full article

(This article belongs to the Special Issue Modern Trends and Application of Decision-Making Theory, Stability and Control, 2nd Edition)

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26 pages, 513 KB

Open AccessArticle

Generation of Extremal Copositive Matrices in Higher Dimensions

by Olga Kostyukova and Tatiana Tchemisova

Axioms 2026, 15(6), 414; https://doi.org/10.3390/axioms15060414 - 2 Jun 2026

Abstract

A fundamental objective in the study of convex cones is the description and analysis of their extreme rays. In the case of the copositive cone, these rays are generated by extremal copositive matrices, which encode the boundary structure of the cone and are [...] Read more.

A fundamental objective in the study of convex cones is the description and analysis of their extreme rays. In the case of the copositive cone, these rays are generated by extremal copositive matrices, which encode the boundary structure of the cone and are closely related to challenging instances of copositive and completely positive programming. In this work, we propose a constructive framework for generating copositive matrices from a given extremal copositive matrix of a smaller order and establish conditions under which copositivity and extremality are preserved. This approach highlights the interplay between the zero structure of a copositive matrix, its minimal zeros, and the facial geometry of the copositive cone. The results obtained allow one to generate new families of extremal copositive matrices in higher dimensions. Full article

(This article belongs to the Section Algebra and Number Theory)

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17 pages, 307 KB

Open AccessArticle

Fuzzy Nilpotent Lie Algebras: Bases, Isomorphisms, and a Measure of Nilpotency

by Giuseppe Filippone, Mario Galici, Gianmarco La Rosa, Federica Piazza and Marco Elio Tabacchi

Axioms 2026, 15(6), 413; https://doi.org/10.3390/axioms15060413 - 2 Jun 2026

Abstract

This paper investigates the structure of fuzzy Lie subalgebras, with particular emphasis on isomorphisms and nilpotency. Building on two prior conference contributions, one of which established foundational results on fuzzy bases of Lie algebras, we develop here a more complete and unified treatment [...] Read more.

This paper investigates the structure of fuzzy Lie subalgebras, with particular emphasis on isomorphisms and nilpotency. Building on two prior conference contributions, one of which established foundational results on fuzzy bases of Lie algebras, we develop here a more complete and unified treatment of these themes. We introduce a notion of isomorphism between fuzzy Lie subalgebras based on the transfer principle via t-cut sets, and we prove that isomorphic fuzzy Lie subalgebras necessarily share the same nilpotency measure. The central contribution of the paper is a fuzzy measure of nilpotency

N (μ) \in [0, 1]

, defined for any non-constant fuzzy Lie subalgebra

μ

of a Lie algebra

g

. This invariant equals 1 precisely when

μ

is fuzzy nilpotent, and decreases as the subalgebra departs from nilpotency. We show that nilpotency of the underlying Lie algebra implies

N (μ) = 1

, but that the converse fails in general, as witnessed by an explicit counterexample. Full article

(This article belongs to the Special Issue New Trends in Fuzzy Logic and Its Applications)

22 pages, 329 KB

Open AccessArticle

Global Strong Solutions to the Vacuum Free Boundary Problem for 1D Liquid Crystal Flow with Degenerate Viscosity

by Tong Li, Junhan Wang and Pan Shi

Axioms 2026, 15(6), 412; https://doi.org/10.3390/axioms15060412 - 1 Jun 2026

Abstract

In this paper, we consider the one-dimensional liquid crystal flow with a vacuum free boundary and a degenerate viscosity coefficient. The global existence and long-time dynamics of strong solutions are established under a smallness condition on the initial energy at the basic level. [...] Read more.

In this paper, we consider the one-dimensional liquid crystal flow with a vacuum free boundary and a degenerate viscosity coefficient. The global existence and long-time dynamics of strong solutions are established under a smallness condition on the initial energy at the basic level. The main challenges come from the degeneracy near the moving boundary and the strong nonlinear coupling between the velocity and the director field. To overcome these, we obtain uniform-in-time and space point-wise bounds of the deformation variable, and we construct uniform-in-time weighted energy estimates via singular multiplier techniques. Unlike previous works, the density is allowed to vanish and the viscosity coefficient is taken to be density-dependent rather than constant. Full article

(This article belongs to the Section Mathematical Physics)

12 pages, 261 KB

Open AccessArticle

A Real Four-Component Integrable Extension of the Standard Kaup–Newell Hierarchy with Two Diagonal Blocks

by Wen-Xiu Ma

Axioms 2026, 15(6), 411; https://doi.org/10.3390/axioms15060411 - 1 Jun 2026

Abstract

This paper aims to introduce a real four-component integrable extension of the complex Kaup–Newell soliton hierarchy. Following a general idea for extending the standard Kaup–Newell spectral matrix, we propose a specific matrix eigenvalue problem involving four real potentials and construct the corresponding integrable [...] Read more.

This paper aims to introduce a real four-component integrable extension of the complex Kaup–Newell soliton hierarchy. Following a general idea for extending the standard Kaup–Newell spectral matrix, we propose a specific matrix eigenvalue problem involving four real potentials and construct the corresponding integrable Hamiltonian hierarchy via the zero-curvature formulation. A recursion operator and a bi-Hamiltonian structure are presented to demonstrate the Liouville integrability of the resulting hierarchy. As an illustrative example, we derive an integrable system of four real derivative nonlinear Schrödinger equations, each containing two linear dispersion terms and generalizing the standard complex derivative nonlinear Schrödinger equations. Full article

(This article belongs to the Topic Advances in Integrable Systems: Theory, Methods and Applications)

16 pages, 362 KB

Open AccessArticle

Secular Perturbations of Translational–Rotational Motion of an Axisymmetric Body in the Restricted Three-Body Problem with Variable Masses

by Alexander Prokopenya, Mukhtar Minglibayev and Balnur Assan

Axioms 2026, 15(6), 410; https://doi.org/10.3390/axioms15060410 - 30 May 2026

Abstract

We consider the translational–rotational motion of a small axisymmetric body in the gravitational field of two stars of variable masses moving under the influence of their mutual gravitational attraction. The two stars are assumed to lose their masses isotropically with different rates and [...] Read more.

We consider the translational–rotational motion of a small axisymmetric body in the gravitational field of two stars of variable masses moving under the influence of their mutual gravitational attraction. The two stars are assumed to lose their masses isotropically with different rates and their total mass decreases according to the joint Meshcherskii law. The relative motion of the stars is described by the corresponding exact solution to Gyldén’s equation and is considered to be given. The small axisymmetric body may change its mass, size and shape while its initial dynamic structure is retained. The problem is analyzed in the framework of Lagrange’s formalism, and equations of translational–rotational motion are derived in terms of the osculating elements of aperiodic motion on quasi-conic sections and the Andoyer variables. As equations of motion of the small body are not integrable, the perturbation theory is applied with the perturbing function expanded into power series in terms of eccentricity and inclination, which are assumed to be small. Averaging these equations over the mean longitudes of the two bodies and two Andoyer angles in the absence of commensurability of frequencies, we obtain the differential equations describing the long-term evolution of the orbital elements and Andoyer variables which may be investigated numerically for different laws of the system parameters’ variation. All the relevant symbolic calculations are performed with the computer algebra system Wolfram Mathematica. Full article

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21 pages, 438 KB

Open AccessArticle

A Fast Chebyshev Spectral Collocation Method for a Coupled System of Nonlinear Klein–Gordon Equations with Caputo Fractional Memory

by Yertay Kazez, Zhanars A. Abdiramanov, Nauryzbay Adil and Abdumauvlen S. Berdyshev

Axioms 2026, 15(6), 409; https://doi.org/10.3390/axioms15060409 - 30 May 2026

Abstract

We develop a fast Chebyshev spectral collocation method for a coupled system of nonlinear Klein–Gordon equations augmented by Caputo-type fractional memory integrals. The governing equations retain the classical second-order time derivative as the leading operator and incorporate weakly singular convolution integrals modelling viscoelastic [...] Read more.

We develop a fast Chebyshev spectral collocation method for a coupled system of nonlinear Klein–Gordon equations augmented by Caputo-type fractional memory integrals. The governing equations retain the classical second-order time derivative as the leading operator and incorporate weakly singular convolution integrals modelling viscoelastic memory damping. The spatial discretisation employs Chebyshev–Gauss–Lobatto collocation, while the temporal integration uses a Newmark scheme (

β_{NM} = 1 / 4

) combined with an implicit–explicit linearisation in which the linear spatial operator is treated implicitly and the nonlinear terms are treated explicitly through a second-order extrapolation. This linearisation eliminates the need for Newton–Raphson iterations at each time step. To overcome the dense memory bottleneck arising from two distinct fractional orders

α \neq β

, the convolution memory kernels are compressed by independent sum-of-exponentials approximations obtained from a double-exponential quadrature of the kernel’s integral representation, which significantly reduces the computational complexity of the history term. A rigorous stability estimate and a global convergence bound are established using a discrete Grönwall inequality. Numerical experiments confirm the theoretical temporal and spatial convergence rates and demonstrate the practical speed-up afforded by the sum-of-exponentials acceleration. A solitary wave collision scenario illustrates the method’s capability to capture asymmetric dispersive wakes generated by the fractional memory. Full article

(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics, 2nd Edition)

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39 pages, 498 KB

Open AccessArticle

Asymptotic Behavior and Construction of Blowing-Up Solutions for a Subcritical Elliptic Problem

by Sarah Alotibi and Mohamed Ben Ayed

Axioms 2026, 15(6), 408; https://doi.org/10.3390/axioms15060408 - 30 May 2026

Abstract

In this paper, we study energy bounded solutions

u_{ε}

converging weakly to 0 of the subcritical problem [...] Read more.

In this paper, we study energy bounded solutions

u_{ε}

converging weakly to 0 of the subcritical problem

- Δ u + g u = h u^{\frac{n + 2}{n - 2} - ε}, u > 0 in Ω, u = 0 on \partial Ω,

where

Ω

is a

C^{2}

bounded domain in

R^{n}

with

n \geq 4

, g is a

C^{1}

positive function on

\bar{Ω}

, h is a

C^{3}

positive function on

\bar{Ω}

, and

ε

is a small positive parameter. Assuming that the normal derivative of h is negative on the boundary, we prove that

u_{ε}

must blow up in the interior of the domain. Moreover, we determine the precise location of the blow-up points and the corresponding blow-up rates. Conversely, for sufficiently small

ε

, we construct blowing-up solutions that converge weakly to zero, which allows us to obtain a multiplicity result for the problem. In contrast, when the normal derivative of h is positive at a boundary point b, we show that it is possible to construct solutions converging to zero and blowing up precisely at b. Full article

(This article belongs to the Section Mathematical Analysis)

13 pages, 359 KB

Open AccessArticle

Global Solvability of a Fifth-Order KdV Equation Posed on Finite Interval [0, d]

by Xiangqing Zhao and Jifeng Bao

Axioms 2026, 15(6), 407; https://doi.org/10.3390/axioms15060407 - 30 May 2026

Abstract

This paper establishes the global existence and uniqueness of solutions to the initial-boundary value problem for a fifth-order KdV equation posed on a finite interval [0, d]. Overcoming the challenge of global solvability imposed by non-conservative boundary conditions, we introduce a nonlinear [...] Read more.

This paper establishes the global existence and uniqueness of solutions to the initial-boundary value problem for a fifth-order KdV equation posed on a finite interval [0, d]. Overcoming the challenge of global solvability imposed by non-conservative boundary conditions, we introduce a nonlinear boundary feedback mechanism inspired by control theory to enforce energy dissipation. The proof hinges on deriving rigorous a priori estimates that capture both the Kato smoothing effect and boundary trace regularity, complemented by a tailored nonlinear estimate to handle the feedback term. Consequently, local solutions are extended to global ones. Furthermore, comprehensive numerical experiments validate the proposed approach and yield strong empirical evidence of exponential energy decay, a property crucial for control applications. Full article

(This article belongs to the Special Issue Advances in Nonlinear Analysis and Boundary Value Problems, 2nd Edition)

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18 pages, 341 KB

Open AccessArticle

Likelihood Ratio Test for Detecting Change Points in the Exponentiated Exponential Logistic Distribution with Applications to Cryptocurrency Data

by Amani S. Alghamdi and Rana A. Alzahrani

Axioms 2026, 15(6), 406; https://doi.org/10.3390/axioms15060406 - 28 May 2026

Abstract

Detecting structural changes or change points in statistical models is a fundamental component of data analysis, as it plays a crucial role in understanding the dynamic behavior of real-world data, particularly in financial markets and cryptocurrency returns. In this study, we developed a [...] Read more.

Detecting structural changes or change points in statistical models is a fundamental component of data analysis, as it plays a crucial role in understanding the dynamic behavior of real-world data, particularly in financial markets and cryptocurrency returns. In this study, we developed a procedure based on the likelihood ratio test (LRT) to identify change points in the parameters of the exponentiated exponential logistic (EEL) distribution. Furthermore, the binary segmentation technique was employed to efficiently detect multiple change points and determine their locations. The proposed methodology was derived under the null and alternative hypotheses, and its statistical properties were examined in depth. To evaluate its performance, extensive Monte Carlo simulations were conducted to assess the empirical power of the test under various sample sizes and significance levels. Furthermore, the method was applied to real cryptocurrency return data to demonstrate its practical ability to detect change points and illustrate its effectiveness at identifying structural breaks. The empirical results indicate that the LRT-based procedure exhibits strong capability in detecting significant distributional changes in cryptocurrency data over time, confirming its effectiveness as an analytical tool in statistical and financial studies. Full article

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18 pages, 332 KB

Open AccessArticle

Intuitionistic Fuzzy

\tilde{\bar{X}} - \tilde{R}

and

\tilde{\bar{X}} - \tilde{S}

Control Charts for Triangular Intuitionistic Fuzzy Numbers

by Gültekin Atalik

Axioms 2026, 15(6), 405; https://doi.org/10.3390/axioms15060405 - 27 May 2026

Abstract

This study proposes a novel methodology for constructing intuitionistic

\tilde{\bar{X}} - \tilde{R}

and

\tilde{\bar{X}} - \tilde{S}

control charts by incorporating a ranking method developed explicitly for triangular intuitionistic fuzzy numbers. Unlike traditional fuzzy control charts, the proposed [...] Read more.

This study proposes a novel methodology for constructing intuitionistic

\tilde{\bar{X}} - \tilde{R}

and

\tilde{\bar{X}} - \tilde{S}

control charts by incorporating a ranking method developed explicitly for triangular intuitionistic fuzzy numbers. Unlike traditional fuzzy control charts, the proposed model eliminates the need for defuzzification in the computation process. Instead, all decisions are derived directly through a fuzzy ranking approach, thereby preserving the integrity of the original fuzzy information and preventing information loss. This characteristic constitutes a key contribution of the study. To validate the practical applicability and effectiveness of the proposed methodology, real-world data collected from an engineering facility were utilized. The results were thoroughly analyzed through a real-world manufacturing case study. The application demonstrated that all samples, except for an assignable cause in one specific sub-range, were statistically in control. Most importantly, the proposed approach monitored the process variations without stripping away the inherent subjective hesitation of the decision-makers, thereby demonstrating its potential capability in handling structural uncertainty compared to traditional crisp methods. Full article

(This article belongs to the Section Logic)

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20 pages, 354 KB

Open AccessArticle

Weighted Composition–Differentiation Operators Between Bers-Type Spaces on Generalized Hua Domains of the First Kind

by Minghua Shi, Jianbing Su and Kang Wang

Axioms 2026, 15(6), 404; https://doi.org/10.3390/axioms15060404 - 27 May 2026

Abstract

This paper investigates weighted composition–differentiation operators acting between Bers-type spaces defined on a generalized Hua domain of the first kind. By establishing a key norm inequality for functions in these spaces, we obtain necessary and sufficient conditions for the boundedness and compactness of [...] Read more.

This paper investigates weighted composition–differentiation operators acting between Bers-type spaces defined on a generalized Hua domain of the first kind. By establishing a key norm inequality for functions in these spaces, we obtain necessary and sufficient conditions for the boundedness and compactness of such operators. Full article

(This article belongs to the Special Issue Recent Advances in Function Spaces and Their Applications)

16 pages, 296 KB

Open AccessArticle

Weak Law of Large Numbers and Mean Convergence for Weighted Sums of Multidimensional Arrays Under Gut’s Condition

by Zhen Wang, Yi Wu and Kai Zhou

Axioms 2026, 15(6), 403; https://doi.org/10.3390/axioms15060403 - 27 May 2026

Abstract

A new concept of weight-array-based stochastic domination in the Cesàro sense is developed. Under Gut’s condition, we establish the weak law of large numbers and

L_{r}

-convergence for weighted sums of multidimensional arrays of pairwise negatively quadrant dependent random variables. These results [...] Read more.

A new concept of weight-array-based stochastic domination in the Cesàro sense is developed. Under Gut’s condition, we establish the weak law of large numbers and

L_{r}

-convergence for weighted sums of multidimensional arrays of pairwise negatively quadrant dependent random variables. These results improve and extend corresponding known results in the literature. Full article

(This article belongs to the Section Mathematical Analysis)

16 pages, 742 KB

Open AccessArticle

A Discrete Version of Local Hausdorff Dimension on Infinite Fractal Networks

by Cheng Zeng, Daohua Wang and Zixuan Zhao

Axioms 2026, 15(6), 402; https://doi.org/10.3390/axioms15060402 - 27 May 2026

Abstract

In this paper, we define the local Hausdorff dimension on fractal networks inspired by the idea of

α

-potential at a point

x \in R^{d}

. We prove some basic properties of the local Hausdorff dimension and then obtain the local Hausdorff [...] Read more.

In this paper, we define the local Hausdorff dimension on fractal networks inspired by the idea of

α

-potential at a point

x \in R^{d}

. We prove some basic properties of the local Hausdorff dimension and then obtain the local Hausdorff dimension of some networks. We also discuss a more generalized dimension definition, namely the subset Hausdorff dimension. Full article

(This article belongs to the Special Issue New Perspective on Fractal Geometry and Its Application)

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15 pages, 14434 KB

Open AccessArticle

q-Close-to-Convexity and Starlikeness of Rabotnov Function

by Saddaf Noreen, Muhammad Imran, Muhey U. Din, Zhang Wei and Adil Murtaza

Axioms 2026, 15(6), 401; https://doi.org/10.3390/axioms15060401 - 26 May 2026

Abstract

The article derives sufficient conditions under which the normalized Rabotnov function becomes q-close-to-convex relative to specific starlike functions on the open unit disk. To enhance the impact of our results, we include some consequences derived from the main theorems, along with graphical [...] Read more.

The article derives sufficient conditions under which the normalized Rabotnov function becomes q-close-to-convex relative to specific starlike functions on the open unit disk. To enhance the impact of our results, we include some consequences derived from the main theorems, along with graphical illustrations. The starlikeness of the Rabotnov function with respect to different aspects also falls within the scope of this study. Full article

(This article belongs to the Special Issue Recent Advances in Complex Analysis and Related Topics)

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23 pages, 519 KB

Open AccessArticle

On the Periodicity and Solvability of Multi-Shift Three-Dimensional Difference Systems

by Yasser Almoteri and Ahmed Ghezal

Axioms 2026, 15(6), 400; https://doi.org/10.3390/axioms15060400 - 26 May 2026

Abstract

This paper investigates the closed-form solvability and dynamical behavior of a class of nonlinear triangular difference systems with overlapping indices, emphasizing the role of coefficient symmetry and asymmetry in determining the qualitative behavior of the system. A unified analytical framework is developed by [...] Read more.

This paper investigates the closed-form solvability and dynamical behavior of a class of nonlinear triangular difference systems with overlapping indices, emphasizing the role of coefficient symmetry and asymmetry in determining the qualitative behavior of the system. A unified analytical framework is developed by transforming the original nonlinear system into equivalent linear or multiplicative difference equations, thereby enabling the derivation of explicit general solutions for various parameter configurations. The results show that the structure of the coefficients plays a fundamental role in determining stability, periodicity, and long-term dynamics. In particular, symmetric configurations tend to produce regular and more structured periodic behavior, whereas asymmetric configurations lead to more irregular oscillatory patterns and increased sensitivity to initial conditions. These theoretical findings are supported by numerical simulations and graphical illustrations, which demonstrate how variations in coefficient values and signs influence the evolution of the system. Finally, an application to discrete survival dynamics is presented, illustrating the capability of the proposed model to describe interacting survival processes under both symmetric and asymmetric parameter regimes, thereby highlighting its potential relevance in the study of applied discrete dynamical systems. Full article

(This article belongs to the Special Issue Difference, Functional, and Related Equations, 2nd Edition)

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18 pages, 324 KB

Open AccessArticle

Hicks-Type Fixed Point Results and Uniform Structure in Intuitionistic Fuzzy b-Metric Spaces

by Şuara Onbaşıoğlu Altuhovs and Banu Pazar Varol

Axioms 2026, 15(6), 399; https://doi.org/10.3390/axioms15060399 - 26 May 2026

Abstract

In this paper, we propose a new class of intuitionistic fuzzy b-metric spaces in the sense of Romaguera and investigate their fixed-point properties. Within this framework, we define and analyze Hicks-type contraction mappings. In addition, the concept of K-stationary intuitionistic fuzzy b-metrics [...] Read more.

In this paper, we propose a new class of intuitionistic fuzzy b-metric spaces in the sense of Romaguera and investigate their fixed-point properties. Within this framework, we define and analyze Hicks-type contraction mappings. In addition, the concept of K-stationary intuitionistic fuzzy b-metrics is introduced and examined through illustrative examples. Our findings generalize classical results in fuzzy b-metric spaces and extend fixed-point theorems to the intuitionistic fuzzy setting. This study enriches fixed-point theory in intuitionistic fuzzy environments and provides a basis for further theoretical investigations and applications. Full article

(This article belongs to the Special Issue New Trends in Fixed Point Theory in Fuzzy Metric Spaces and Their Generalizations)

13 pages, 265 KB

Open AccessArticle

Trans-Sasakian Structures with Certain Restrictions

by Sharief Deshmukh and Amira Ishan

Axioms 2026, 15(6), 398; https://doi.org/10.3390/axioms15060398 - 25 May 2026

Abstract

We find restrictions on a trans-Sasakian structure

(F, u, γ, α, β)

on a 3-dimensional Riemannian manifold

(M^{3}, g)

so that

(M^{3}, g)

is homothetic to a Sasakian manifold. In that, first we show that [...] Read more.

We find restrictions on a trans-Sasakian structure

(F, u, γ, α, β)

on a 3-dimensional Riemannian manifold

(M^{3}, g)

so that

(M^{3}, g)

is homothetic to a Sasakian manifold. In that, first we show that if the vector

u

of the trans-Sasakian structure

(F, u, γ, α, β)

on a 3-dimensional Riemannian manifold

(M^{3}, g)

is an affine conformal vector with affine potential

α \neq 0

and the condition

u (α) = - β^{2}

holds, necessarily implies

(M^{3}, g)

is homothetic to a Sasakian manifold. Similarly, it is shown that if the vector

u

of the trans-Sasakian structure

(F, u, γ, α, β)

on a 3-dimensional Riemannian manifold

(M^{3}, g)

is a projective vector and the sectional curvatures of the plane sections containing

u

are positive constant, then

(M^{3}, g)

is homothetic to a Sasakian manifold. Finally, we find certain generic conditions on a 3-dimensional Riemannian manifold

(M^{3}, g)

possessing a trans-Sasakian structure

(F, u, γ, α, β)

so that

(M^{3}, g)

is homothetic to a Sasakian manifold. Full article

(This article belongs to the Special Issue Differential Geometry and Its Application, 4th Edition)

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