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Axioms
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Trends in Differential Geometry and Algebraic Topology, 2nd Edition
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Trends in Differential Geometry and Algebraic Topology, 2nd Edition

A Special Issue of Axioms (ISSN 2075-1680) belonging to the section "Geometry and Topology".

Deadline for manuscript submissions: 30 March 2027 | Viewed by 3212

Editor

Dr. Byungdo Park

E-Mail Website
Guest Editor
Department of Mathematics Education, Chungbuk National University, Cheongju 28644, Republic of Korea
Interests: differential geometry and algebraic topology; geometric structures on higher bundles; generalized cohomology theories and their equivariant, differential, and twisted refinements
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We are pleased to invite you to contribute to a Special Issue of Axioms titled "Trends in Differential Geometry and Algebraic Topology, 2nd Edition." This issue aims to showcase cutting-edge research and novel perspectives at the intersection of these two fundamental areas of mathematics.

As a recognized expert in the field, your contribution would be invaluable in shaping the discourse on recent developments and future directions. We welcome original research articles, comprehensive reviews, and insightful perspectives that explore the following:

  • Advances in differential geometric structures and their applications, including Riemannian and symplectic geometry;
  • Higher category theory, homotopy theory, homology theory, algebraic K-theory;
  • Interplay between differential geometry and algebraic topology;
  • Index theory, noncommutative geometry;
  • Emerging computational methods in geometric and topological analysis;
  • Applications of differential geometry and algebraic topology in physics, data science, or other disciplines.

We are excited about the possibility of featuring your work in this Special Issue and contributing to the advancement of these vital mathematical fields.

We look forward to the prospect of your valuable contribution.

Dr. Byungdo Park
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • differential geometry
  • algebraic topology
  • Riemannian geometry
  • symplectic geometry
  • symplectic topology
  • homotopy algebra
  • homotopy theory
  • homology theory
  • category theory
  • algebraic K-theory
  • topological K-theory
  • index theory
  • noncommutative geometry
  • string theory
  • quantum field theory

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  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (5 papers)

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Research

18 pages, 322 KB  
Article
Geometric Decomposition of Force and Yank for Variable-Mass Systems in Minkowski 3-Space
by Fatimah Alghamdi and Ayman Elsharkawy
Axioms 2026, 15(7), 526; https://doi.org/10.3390/axioms15070526 - 14 Jul 2026
Viewed by 273
Abstract
We develop a differential-geometric framework for variable-mass particles moving along non-lightlike curves with non-vanishing curvature in Minkowski 3-space E13, employing the Frenet–Serret apparatus adapted to a Lorentzian signature. The force is defined as the time derivative of momentum, [...] Read more.
We develop a differential-geometric framework for variable-mass particles moving along non-lightlike curves with non-vanishing curvature in Minkowski 3-space E13, employing the Frenet–Serret apparatus adapted to a Lorentzian signature. The force is defined as the time derivative of momentum, F=d(mv)/dt, incorporating mass variation through a Meshchersky-type reactive term; no covariant four-momentum formulation is assumed. Explicit closed-form expressions are derived for the momentum vector P(t), force F(t), and yank Y(t)=dF/dt for three distinct causal types of regular Frenet curves: spacelike curves with a spacelike principal normal, spacelike curves with a timelike principal normal, and timelike curves. The tangential yank component carries the causal sign factor δB, reflecting the type of curve. A theorem on the evolution of kinetic energy separates the inertial contribution mvv˙ from the reactive contribution 12m˙v2 due to mass variation. A radial decomposition of the force in the osculating plane generalizes Siacci’s classical theorem to Lorentzian geometry and variable-mass systems. When the rectifying coordinate b is non-zero, a corresponding decomposition of the yank is also obtained. Three illustrative physical scenarios are discussed: rocket motion with variable mass (with potential future relevance to trajectory prediction, stability analysis, and motion-anomaly assessment in unmanned systems), a geometric analogy for orbital parameter changes, and particle motion in a magnetic monopole field. Two fully worked examples (a Lorentzian helix and a logarithmic spiral) provide explicit closed-form expressions for all geometric and dynamical quantities, accompanied by numerical plots. The results recover the Euclidean case in the appropriate signature limit. Full article
(This article belongs to the Special Issue Trends in Differential Geometry and Algebraic Topology, 2nd Edition)
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14 pages, 321 KB  
Article
Ricci Semi-Symmetric Bulk Viscous String Fluid Spacetime in F(R,T)-Gravity and Energy Constraints for Penrose Theorem
by Mohd Danish Siddiqi, Ibrahim Al-Dayel and Sharief Deshmukh
Axioms 2026, 15(7), 488; https://doi.org/10.3390/axioms15070488 - 29 Jun 2026
Viewed by 277
Abstract
This study is dedicated to a separable F(R,T)-gravity related to the bulk viscous string fluid to extract the equation of state for F(R,T)-gravity. In this research, we offer an insight into [...] Read more.
This study is dedicated to a separable F(R,T)-gravity related to the bulk viscous string fluid to extract the equation of state for F(R,T)-gravity. In this research, we offer an insight into calculating the density and pressure in terms of string tension in the phantom barrier, stiff fluid, and matter-dominated eras. As demonstrated, if a spacetime in F(R,T)-gravity is full of bulk viscous string fluid matter, it is a generalized quasi-Einstein spacetime. In addition, we determine the equation of state of Ricci semi-symmetric and Ricci pseudo-symmetric spacetime in F(R,T)-gravity filled with bulk viscous string fluid matter. Finally, we try to give the energy constraints in view of Penrose’s singularity theorem of black holes for the spacetime in F(R,T)-gravity attached to bulk viscous string fluid. Full article
(This article belongs to the Special Issue Trends in Differential Geometry and Algebraic Topology, 2nd Edition)
17 pages, 269 KB  
Article
Classification of Invariant 2-Conformal Vector Fields on 4D Non-Reductive Homogeneous Spaces
by Bang-Yen Chen, Foued Aloui, Majid Ali Choudhary and Ibrahim Al-Dayel
Axioms 2026, 15(5), 353; https://doi.org/10.3390/axioms15050353 - 10 May 2026
Cited by 1 | Viewed by 370
Abstract
The notion of 2-conformal vector fields on pseudo-Riemannian manifolds, which arose naturally in the study of hyperbolic solitons, is introduced by Fasihi-Ramandi, De, and Shamkhali. In this paper, we study invariant 2-conformal vector fields on four-dimensional non-reductive pseudo-Riemannian homogeneous manifolds G/H [...] Read more.
The notion of 2-conformal vector fields on pseudo-Riemannian manifolds, which arose naturally in the study of hyperbolic solitons, is introduced by Fasihi-Ramandi, De, and Shamkhali. In this paper, we study invariant 2-conformal vector fields on four-dimensional non-reductive pseudo-Riemannian homogeneous manifolds G/H. Consequently, the complete classification of such vector fields is achieved, together with the necessary and sufficient conditions for their existence. The results are then applied to Lorentzian and neutral signatures, where 2-conformal vector fields provide an effective criterion for detecting 2-conformal equivalences in geometries with limited algebraic symmetries. Full article
(This article belongs to the Special Issue Trends in Differential Geometry and Algebraic Topology, 2nd Edition)
15 pages, 318 KB  
Article
Chen-Type Inequalities for PS-Submanifolds in Complex Space Forms
by Md Aquib
Axioms 2026, 15(5), 339; https://doi.org/10.3390/axioms15050339 - 5 May 2026
Cited by 1 | Viewed by 389
Abstract
In this paper, we investigate Chen’s δ-invariant for partially slant (PS) submanifolds of complex space forms. A PS-submanifold admits an orthogonal decomposition of the tangent bundle into a proper slant distribution and an arbitrary ambiguous distribution. Using the Gauss equation together with [...] Read more.
In this paper, we investigate Chen’s δ-invariant for partially slant (PS) submanifolds of complex space forms. A PS-submanifold admits an orthogonal decomposition of the tangent bundle into a proper slant distribution and an arbitrary ambiguous distribution. Using the Gauss equation together with algebraic optimization techniques, we derive a Chen-type inequality relating the δ-invariant to the squared mean curvature, the holomorphic sectional curvature of the ambient space, and the slant angle of the slant distribution. Unlike the classical Chen inequality for slant submanifolds, the obtained estimate contains an additional term reflecting the contribution of the ambiguous distribution. Several corollaries are derived, including dimension-dependent bounds and special cases corresponding to hemi-slant and semi-slant submanifolds. The equality case is also characterized in terms of the structure of the shape operators. These results provide a natural extension of Chen-type inequalities to the broader framework of partially slant geometry in Kähler manifolds. Full article
(This article belongs to the Special Issue Trends in Differential Geometry and Algebraic Topology, 2nd Edition)
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20 pages, 306 KB  
Article
Intrinsic and Extrinsic Geometry of Pseudoparallel Submanifolds in Almost Kenmotsu (κ, μ, ν)-Manifolds
by Ibrahim Al-Dayel, Tuğba Mert and Mohd Danish Siddiqi
Axioms 2026, 15(2), 146; https://doi.org/10.3390/axioms15020146 - 16 Feb 2026
Viewed by 1231
Abstract
In this paper, we undertake a detailed study of pseudoparallel submanifolds of almost Kenmotsu (κ,μ,ν)-spaces, with particular emphasis on invariant submanifolds. By employing the W0 and W1 curvature tensors, we analyze several classes of [...] Read more.
In this paper, we undertake a detailed study of pseudoparallel submanifolds of almost Kenmotsu (κ,μ,ν)-spaces, with particular emphasis on invariant submanifolds. By employing the W0 and W1 curvature tensors, we analyze several classes of pseudoparallel submanifolds, including Ricci-generalized pseudoparallel ones, and investigate how these curvature conditions influence the intrinsic and extrinsic geometry of the submanifolds. One of the main contributions of this work is the derivation of necessary and sufficient conditions under which invariant pseudoparallel submanifolds of almost Kenmotsu (κ,μ,ν)-spaces become totally geodesic. In particular, the use of the W0 and W1 curvature tensors provides a unified and effective framework for characterizing total geodesicity in this geometric setting. Furthermore, we obtain new and significant classification results by explicitly relating the total geodesicity of invariant submanifolds to the structural functions κ, μ and ν. These results not only generalize several known characterizations in the literature but also yield novel geometric insights into the structure of pseudoparallel submanifolds in almost Kenmotsu (κ,μ,ν)-spaces. We also provide an example to support our concept. Full article
(This article belongs to the Special Issue Trends in Differential Geometry and Algebraic Topology, 2nd Edition)
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