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17 pages, 351 KiB

Open AccessArticle

Special Curves and Tubes in the BCV-Sasakian Manifold

by Tuba Ağırman Aydın and Ensar Ağırman

Symmetry 2025, 17(8), 1215; https://doi.org/10.3390/sym17081215 - 1 Aug 2025

Viewed by 158

In this study, theorems and proofs related to spherical and focal curves are presented in the BCV-Sasakian space. An approximate solution to the differential equation characterizing spherical curves in the BCV-Sasakian manifold

M^{3}

is obtained using the Taylor matrix collocation method. The [...] Read more.

In this study, theorems and proofs related to spherical and focal curves are presented in the BCV-Sasakian space. An approximate solution to the differential equation characterizing spherical curves in the BCV-Sasakian manifold

M^{3}

is obtained using the Taylor matrix collocation method. The general equations of canal and tubular surfaces are provided within this geometric framework. Additionally, the curvature properties of the tubular surface constructed around a non-vertex focal curve are computed and analyzed. All of these results are presented for the first time in the literature within the context of the BCV-Sasakian geometry. Thus, this study makes a substantial contribution to the differential geometry of contact metric manifolds by extending classical concepts into a more generalized and complex geometric structure. Full article

(This article belongs to the Section Mathematics)

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17 pages, 279 KiB

Open AccessArticle

CL-Transformation on 3-Dimensional Quasi Sasakian Manifolds and Their Ricci Soliton

by Rajesh Kumar, Lalnunenga Colney and Dalal Alhwikem

Mathematics 2025, 13(10), 1543; https://doi.org/10.3390/math13101543 - 8 May 2025

Viewed by 336

Abstract

This paper explores the geometry of 3-dimensional quasi Sasakian manifolds under CL-transformations. We construct both infinitesimal and

C L

-transformation and demonstrate that the former does not necessarily yield projective killing vector fields. A novel invariant tensor, termed the

C L

-curvature [...] Read more.

This paper explores the geometry of 3-dimensional quasi Sasakian manifolds under CL-transformations. We construct both infinitesimal and

C L

-transformation and demonstrate that the former does not necessarily yield projective killing vector fields. A novel invariant tensor, termed the

C L

-curvature tensor, is introduced and shown to remain invariant under

C L

-transformations. Utilizing this tensor, we characterize

C L

-flat,

C L

-symmetric,

C L

-

φ

symmetric and

C L

-

φ

recurrent structures on such manifolds by mean of differential equations. Furthermore, we investigate conditions under which a Ricci soliton exists on a CL-transformed quasi Sasakian manifold, revealing that under flat curvature, the structure becomes Einstein. These findings contribute to the understanding of curvature dynamics and soliton theory within the context of contact metric geometry. Full article

6 pages, 177 KiB

Open AccessEditorial

Differentiable Manifolds and Geometric Structures

by Adara M. Blaga

Mathematics 2025, 13(7), 1082; https://doi.org/10.3390/math13071082 - 26 Mar 2025

Viewed by 428

Abstract

This editorial presents 26 research articles published in the Special Issue entitled Differentiable Manifolds and Geometric Structures of the MDPI Mathematics journal, which covers a wide range of topics particularly from the geometry of (pseudo-)Riemannian manifolds and their submanifolds, providing some of the [...] Read more.

This editorial presents 26 research articles published in the Special Issue entitled Differentiable Manifolds and Geometric Structures of the MDPI Mathematics journal, which covers a wide range of topics particularly from the geometry of (pseudo-)Riemannian manifolds and their submanifolds, providing some of the latest achievements in different areas of differential geometry, among which is counted: the geometry of differentiable manifolds with curvature restrictions such as Golden space forms, Sasakian space forms; diffeological and affine connection spaces; Weingarten and Delaunay surfaces; Chen-type inequalities for submanifolds; statistical submersions; manifolds endowed with different geometric structures (Sasakian, weak nearly Sasakian, weak nearly cosymplectic, LP-Kenmotsu, paraquaternionic); solitons (almost Ricci solitons, almost Ricci–Bourguignon solitons, gradient r-almost Newton–Ricci–Yamabe solitons, statistical solitons, solitons with semi-symmetric connections); vector fields (projective, conformal, Killing, 2-Killing) [...] Full article

(This article belongs to the Special Issue Differentiable Manifolds and Geometric Structures)

16 pages, 266 KiB

Open AccessArticle

Geometry of LP-Sasakian Manifolds Admitting a General Connection

by Rajesh Kumar, Laltluangkima Chawngthu, Oğuzhan Bahadır and Meraj Ali Khan

Mathematics 2025, 13(6), 902; https://doi.org/10.3390/math13060902 - 7 Mar 2025

Viewed by 592

Abstract

This paper concerns certain properties of projective curvature tensor, conharmonic curvature tensor, quasi-conharmonic curvature tensor, and Ricci semi-symmetric conditions with respect to the general connection in an LP-Sasakian manifold. We also provide the applications of LP-Sasakian manifolds admitting general connections in the context [...] Read more.

This paper concerns certain properties of projective curvature tensor, conharmonic curvature tensor, quasi-conharmonic curvature tensor, and Ricci semi-symmetric conditions with respect to the general connection in an LP-Sasakian manifold. We also provide the applications of LP-Sasakian manifolds admitting general connections in the context of the general theory of relativity. Full article

(This article belongs to the Special Issue Differential Geometry, Geometric Analysis and Their Related Applications)

14 pages, 268 KiB

Open AccessArticle

Ricci–Yamabe Solitons on Sasakian Manifolds with the Generalized Tanaka–Webster Connection

by Abdul Haseeb

AppliedMath 2025, 5(1), 22; https://doi.org/10.3390/appliedmath5010022 - 3 Mar 2025

Viewed by 580

Abstract

In this article, we analyze some curvature restrictions satisfying by the concircular curvature tensor in

(2 n + 1)

-dimensional Sasakian manifolds with the generalized Tanaka–Webster connection

\bar{\nabla}

admitting Ricci–Yamabe solitons. Finally, we give an example of three-dimensional Sasakian manifolds [...] Read more.

In this article, we analyze some curvature restrictions satisfying by the concircular curvature tensor in

(2 n + 1)

-dimensional Sasakian manifolds with the generalized Tanaka–Webster connection

\bar{\nabla}

admitting Ricci–Yamabe solitons. Finally, we give an example of three-dimensional Sasakian manifolds which verifies some of our findings. Full article

(This article belongs to the Special Issue Advances in Iterative Methods and Stability Analysis for Solving Nonlinear Problems)

14 pages, 276 KiB

Open AccessArticle

Eigenvalues for the Generalized Laplace Operator of Slant Submanifolds in the Sasakian Space Forms Admitting Semi-Symmetric Metric Connection

by Ibrahim Al-Dayel, Meraj Ali Khan and Sudhakar Kumar Chaubey

Symmetry 2025, 17(2), 279; https://doi.org/10.3390/sym17020279 - 11 Feb 2025

Viewed by 510

Abstract

This study is focused on pioneering new upper bounds on mean curvature and constant sectional curvature relative to the first positive eigenvalue of the generalized Laplacian operator in the differentiable manifolds with a semi-symmetric metric connection. Multiple approaches are being explored to determine [...] Read more.

This study is focused on pioneering new upper bounds on mean curvature and constant sectional curvature relative to the first positive eigenvalue of the generalized Laplacian operator in the differentiable manifolds with a semi-symmetric metric connection. Multiple approaches are being explored to determine the principal eigenvalue for the generalized-Laplacian operator in closed oriented-slant submanifolds within a Sasakian space form (ssf) with a semi-symmetric metric (ssm) connection. By utilizing our findings on the Laplacian, we extend several Reilly-type inequalities to the generalized Laplacian on slant submanifolds within a unit sphere with a semi-symmetric metric (ssm) connection. The research is concluded with a detailed examination of specific scenarios. Full article

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

18 pages, 300 KiB

Open AccessArticle

Magnetic Curves in Homothetic s-th Sasakian Manifolds

by Şaban Güvenç and Cihan Özgür

Mathematics 2025, 13(1), 159; https://doi.org/10.3390/math13010159 - 4 Jan 2025

Viewed by 701

Abstract

We investigate normal magnetic curves in

(2 n + s)

-dimensional homothetic s-th Sasakian manifolds as a generalization of S-manifolds. We show that a curve

γ

is a normal magnetic curve in a homothetic s-th Sasakian manifold if [...] Read more.

We investigate normal magnetic curves in

(2 n + s)

-dimensional homothetic s-th Sasakian manifolds as a generalization of S-manifolds. We show that a curve

γ

is a normal magnetic curve in a homothetic s-th Sasakian manifold if and only if its osculating order satisfies

r \leq 3

and it belongs to a family of

θ_{i}

-slant helices. Additionally, we construct a homothetic s-th Sasakian manifold using generalized D-homothetic transformations and present the parametric equations of normal magnetic curves in this manifold. Full article

(This article belongs to the Special Issue Differentiable Manifolds and Geometric Structures)

13 pages, 264 KiB

Open AccessArticle

Applications of Disaffinity Vectors to Certain Riemannian Manifolds

by Hanan Alohali, Sharief Deshmukh and Bang-Yen Chen

Mathematics 2024, 12(24), 3951; https://doi.org/10.3390/math12243951 - 16 Dec 2024

Viewed by 664

Abstract

A disaffinity vector on a Riemannian manifold is a vector field whose affinity tensor vanishes. In this paper, we prove that every disaffinity vector on a compact Riemannian manifold is an incompressible vector field. Then, we discover a sufficient condition for an incompressible [...] Read more.

A disaffinity vector on a Riemannian manifold is a vector field whose affinity tensor vanishes. In this paper, we prove that every disaffinity vector on a compact Riemannian manifold is an incompressible vector field. Then, we discover a sufficient condition for an incompressible vector field to be disaffinity. Next, we study trans-Sasakian 3-manifolds whose Reeb vector field is disaffinity and obtain two sufficient conditions for a trans-Sasakian 3-manifold to be homothetic to a Sasakian 3-manifold. Finally, we prove that a complete Riemannian manifold admitting a non-harmonic disaffinity function satisfying the Eikonal equation and a Ricci curvature inequality is isometric to a Euclidean space. Full article

(This article belongs to the Special Issue Recent Studies in Differential Geometry and Its Applications)

18 pages, 346 KiB

Open AccessFeature PaperArticle

Pinching Results for Submanifolds in Lorentzian–Sasakian Manifolds Endowed with a Semi-Symmetric Non-Metric Connection

by Mohammed Mohammed, Ion Mihai and Andreea Olteanu

Mathematics 2024, 12(23), 3651; https://doi.org/10.3390/math12233651 - 21 Nov 2024

Viewed by 844

Abstract

We establish an improved Chen inequality involving scalar curvature and mean curvature and geometric inequalities for Casorati curvatures, on slant submanifolds in a Lorentzian–Sasakian space form endowed with a semi-symmetric non-metric connection. Also, we present examples of slant submanifolds in a Lorentzian–Sasakian space [...] Read more.

We establish an improved Chen inequality involving scalar curvature and mean curvature and geometric inequalities for Casorati curvatures, on slant submanifolds in a Lorentzian–Sasakian space form endowed with a semi-symmetric non-metric connection. Also, we present examples of slant submanifolds in a Lorentzian–Sasakian space form. Full article

(This article belongs to the Special Issue Recent Studies in Differential Geometry and Its Applications)

12 pages, 271 KiB

Open AccessArticle

A Conformal η-Ricci Soliton on a Four-Dimensional Lorentzian Para-Sasakian Manifold

by Yanlin Li, Arup Kumar Mallick, Arindam Bhattacharyya and Mića S. Stanković

Axioms 2024, 13(11), 753; https://doi.org/10.3390/axioms13110753 - 31 Oct 2024

Cited by 11 | Viewed by 874

Abstract

This paper focuses on some geometrical and physical properties of a conformal η-Ricci soliton (Cη-RS) on a four-dimension Lorentzian Para-Sasakian (LP-S) manifold. The first section presents an introduction to Cη-RS on LP-S manifolds, followed by a discussion of [...] Read more.

This paper focuses on some geometrical and physical properties of a conformal η-Ricci soliton (Cη-RS) on a four-dimension Lorentzian Para-Sasakian (LP-S) manifold. The first section presents an introduction to Cη-RS on LP-S manifolds, followed by a discussion of preliminary ideas about the LP-Sasakian manifold. In the subsequent sections, we establish several results pertaining to four-dimension LP-S manifolds that exhibit Cη-RS. Additionally, we consider certain conditions associated with Cη-RS on four-dimension LP-S manifolds. Besides these geometrical points of view, we consider this soliton in a perfect fluid spacetime and obtain some interesting physical properties. Finally, we present a case study of a Cη-RS on a four-dimension LP-S manifold. Full article

(This article belongs to the Special Issue Advances in Differential Geometry and Mathematical Physics)

9 pages, 264 KiB

Open AccessArticle

Weak Quasi-Contact Metric Manifolds and New Characteristics of K-Contact and Sasakian Manifolds

by Vladimir Rovenski

Mathematics 2024, 12(20), 3230; https://doi.org/10.3390/math12203230 - 15 Oct 2024

Viewed by 1704

Abstract

Quasi-contact metric manifolds (introduced by Y. Tashiro and then studied by several authors) are a natural extension of contact metric manifolds. Weak almost-contact metric manifolds, i.e., where the linear complex structure on the contact distribution is replaced by a nonsingular skew-symmetric tensor, have [...] Read more.

Quasi-contact metric manifolds (introduced by Y. Tashiro and then studied by several authors) are a natural extension of contact metric manifolds. Weak almost-contact metric manifolds, i.e., where the linear complex structure on the contact distribution is replaced by a nonsingular skew-symmetric tensor, have been defined by the author and R. Wolak. In this paper, we study a weak analogue of quasi-contact metric manifolds. Our main results generalize some well-known theorems and provide new criterions for K-contact and Sasakian manifolds in terms of conditions on the curvature tensor and other geometric objects associated with the weak quasi-contact metric structure. Full article

(This article belongs to the Special Issue Differential Geometric Structures and Their Applications)

28 pages, 407 KiB

Open AccessArticle

Continuity Equation of Transverse Kähler Metrics on Sasakian Manifolds

by Yushuang Fan and Tao Zheng

Mathematics 2024, 12(19), 3132; https://doi.org/10.3390/math12193132 - 7 Oct 2024

Viewed by 901

Abstract

We introduce the continuity equation of transverse Kähler metrics on Sasakian manifolds and establish its interval of maximal existence. When the first basic Chern class is null (resp. negative), we prove that the solution of the (resp. normalized) continuity equation converges smoothly to [...] Read more.

We introduce the continuity equation of transverse Kähler metrics on Sasakian manifolds and establish its interval of maximal existence. When the first basic Chern class is null (resp. negative), we prove that the solution of the (resp. normalized) continuity equation converges smoothly to the unique

η

-Einstein metric in the basic Bott–Chern cohomological class of the initial transverse Kähler metric (resp. first basic Chern class). These results are the transverse version of the continuity equation of the Kähler metrics studied by La Nave and Tian, and also counterparts of the Sasaki–Ricci flow studied by Smoczyk, Wang, and Zhang. Full article

(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory, 2nd Edition)

11 pages, 281 KiB

Open AccessArticle

Solitonical Inequality on Submanifolds in Trans-Sasakian Manifolds Coupled with a Slant Factor

by Mohd Danish Siddiqi and Rawan Bossly

Axioms 2024, 13(6), 370; https://doi.org/10.3390/axioms13060370 - 30 May 2024

Viewed by 706

Abstract

In this article, we study the Ricci soliton on slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection. Moreover, we derive a lower-bound-type inequality for the slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection in terms of gradient [...] Read more.

In this article, we study the Ricci soliton on slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection. Moreover, we derive a lower-bound-type inequality for the slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection in terms of gradient Ricci solitons. We also characterize anti-invariant, invariant, quasi-umbilical submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection for which the same inequality case holds. Finally, we deduce the above inequalities in terms of a scalar concircular field on submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection. Full article

(This article belongs to the Special Issue Advances in Differential Geometry and Singularity Theory)

16 pages, 299 KiB

Open AccessArticle

Some Chen Inequalities for Submanifolds in Trans-Sasakian Manifolds Admitting a Semi-Symmetric Non-Metric Connection

by Mohammed Mohammed, Fortuné Massamba, Ion Mihai, Abd Elmotaleb A. M. A. Elamin and M. Saif Aldien

Axioms 2024, 13(3), 195; https://doi.org/10.3390/axioms13030195 - 15 Mar 2024

Cited by 1 | Viewed by 1884

Abstract

In the present article, we study submanifolds tangent to the Reeb vector field in trans-Sasakian manifolds. We prove Chen’s first inequality and the Chen–Ricci inequality, respectively, for such submanifolds in trans-Sasakian manifolds which admit a semi-symmetric non-metric connection. Moreover, a generalized Euler inequality [...] Read more.

In the present article, we study submanifolds tangent to the Reeb vector field in trans-Sasakian manifolds. We prove Chen’s first inequality and the Chen–Ricci inequality, respectively, for such submanifolds in trans-Sasakian manifolds which admit a semi-symmetric non-metric connection. Moreover, a generalized Euler inequality for special contact slant submanifolds in trans-Sasakian manifolds endowed with a semi-symmetric non-metric connection is obtained. Full article

(This article belongs to the Special Issue Differential Geometry and Its Application, 2nd Edition)

13 pages, 259 KiB

Open AccessArticle

Contact CR-Warped Product Submanifold of a Sasakian Space Form with a Semi-Symmetric Metric Connection

by Meraj Ali Khan, Ibrahim Al-Dayel, Foued Aloui and Shyamal Kumar Hui

Symmetry 2024, 16(2), 190; https://doi.org/10.3390/sym16020190 - 6 Feb 2024

Cited by 1 | Viewed by 1313

Abstract

The main goal of this research paper is to investigate contact CR-warped product submanifolds within Sasakian space forms, utilizing a semi-symmetric metric connection. We conduct a comprehensive analysis of these submanifolds and establish several significant results. Additionally, we formulate an inequality that establishes [...] Read more.

The main goal of this research paper is to investigate contact CR-warped product submanifolds within Sasakian space forms, utilizing a semi-symmetric metric connection. We conduct a comprehensive analysis of these submanifolds and establish several significant results. Additionally, we formulate an inequality that establishes a relationship between the squared norm of the second fundamental form and the warping function. Lastly, we present a number of geometric applications derived from our findings. Full article

(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology, 3rd Edition)

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