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Axioms
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Differential Geometry and Its Application, 3rd Edition
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Differential Geometry and Its Application, 3rd Edition

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Geometry and Topology".

Deadline for manuscript submissions: 30 November 2025 | Viewed by 3601

Special Issue Editor

Prof. Dr. Mica Stankovic

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Sciences and Mathematics, University of Nis, 18000 Niš, Serbia
Interests: Riemannian geometry; spaces of non-symmetric affine connection; geodesic mappings; Finsler geometry; infinitesimal bending; almost geodesic mappings; Kahlerian spaces
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is a continuation of our previous Special Issue on "Differential Geometry and Its Application, 2nd edition". Our intention is to launch a Special Edition of Axioms in which the central theme would be the generalization of Riemann spaces and their mappings.

We wish to provide an opportunity to present the latest achievements in many branches of theoretical and practical studies of mathematics, which are related to the theory of Riemann and generalized Riemann spaces and their mappings.

Among the topics that will be included in this Special Issue, we can consider the following non-exhaustive list:

Riemannian spaces and generalizations, Kenmotsu manifolds, Kaehler manifolds, manifolds with non-symmetric linear connections, co-symplectic manifolds, contact manifolds, statistical manifolds, Minkowski spaces, geodesic mappings, almost geodesic mappings, holomorphically projective mappings, warped product of manifolds, complex space forms, quaternionic space forms, golden manifolds, inequalities, invariants, immersions, etc.

In addition to the above topics, new ideas are also welcome.

In the hope that this initiative will be of interest, we encourage you to submit your current research for inclusion in this Special Issue.

Prof. Dr. Mica Stankovic
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 100 words) can be sent to the Editorial Office for announcement on this website.

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-blind 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

  • contact manifolds
  • generalized Riemann spaces
  • statistical manifolds
  • kenmotsu manifolds
  • kaehler manifolds
  • golden manifolds
  • invariants
  • immersions
  • complex space forms
  • geodesic mappings

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Related Special Issues

Published Papers (7 papers)

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Research

16 pages, 260 KiB  
Article
Geometric and Physical Characteristics of Pseudo-Schouten Symmetric Manifolds
by Mohabbat Ali, Mohd Vasiulla and Meraj Ali Khan
Axioms 2025, 14(4), 256; https://doi.org/10.3390/axioms14040256 - 28 Mar 2025
Viewed by 188
Abstract
In this paper, we introduce and conduct a comprehensive study of pseudo-Schouten symmetric manifolds (PSS)n. We establish necessary and sufficient conditions for such a manifold to be Einstein and quasi-Einstein, respectively. Next, we examine pseudo-Schouten symmetric spacetimes [...] Read more.
In this paper, we introduce and conduct a comprehensive study of pseudo-Schouten symmetric manifolds (PSS)n. We establish necessary and sufficient conditions for such a manifold to be Einstein and quasi-Einstein, respectively. Next, we examine pseudo-Schouten symmetric spacetimes within the framework of general relativity. Furthermore, we investigate their role in relativistic spacetime models by considering Einstein’s field equations with and without a cosmological constant. We also show that pseudo-Schouten symmetric spacetimes satisfying Einstein’s equations with a quadratic Killing energy–momentum tensor or a Codazzi-type energy–momentum tensor cannot have non-zero constant scalar curvature. Finally, the existence of pseudo-Schouten symmetric spacetime is shown by constructing an explicit non-trivial example. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application, 3rd Edition)
16 pages, 497 KiB  
Article
Generalized Bertrand Curve Pairs in Euclidean Four-Dimensional Space
by Yanlin Li, Osman Keçilioğlu and Kazım İlarslan
Axioms 2025, 14(4), 253; https://doi.org/10.3390/axioms14040253 - 27 Mar 2025
Viewed by 149
Abstract
In this study, the existence of Bertrand curves (in the classical sense, i.e., curves with a common principal normal vector field) in four-dimensional Euclidean space is demonstrated using a novel approach. The necessary conditions for a regular curve to be a Bertrand curve [...] Read more.
In this study, the existence of Bertrand curves (in the classical sense, i.e., curves with a common principal normal vector field) in four-dimensional Euclidean space is demonstrated using a novel approach. The necessary conditions for a regular curve to be a Bertrand curve pair are obtained. Furthermore, the relationship between Bertrand curves and Combescure-related curves (pairs of curves with parallel Frenet vectors) is established, and several geometric properties are derived. Additionally, examples are constructed for both Bertrand curve pairs and Combescure-related curve pairs, and their orthogonal projections onto three-dimensional subspaces of four-dimensional space are visualized. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application, 3rd Edition)
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14 pages, 240 KiB  
Article
Analysis of Screen Generic Lightlike Submanifolds in an Indefinite Kaehler Statistical Manifold Endowed with a Quarter-Symmetric Non-Metric Connection
by Vandana Gupta, Jasleen Kaur, Oğuzhan Bahadır and Meraj Ali Khan
Axioms 2025, 14(3), 200; https://doi.org/10.3390/axioms14030200 - 8 Mar 2025
Viewed by 430
Abstract
This paper introduces the notion of screen generic lightlike submanifolds (SGLSs) of an indefinite Kaehler statistical manifold equipped with a quarter-symmetric non-metric (QSNM) connection, supported by suitable illustrations. Assertions for induced connection on the lightlike submanifold and integrability of the distributions are proved. [...] Read more.
This paper introduces the notion of screen generic lightlike submanifolds (SGLSs) of an indefinite Kaehler statistical manifold equipped with a quarter-symmetric non-metric (QSNM) connection, supported by suitable illustrations. Assertions for induced connection on the lightlike submanifold and integrability of the distributions are proved. The characterization theorems on parallelism and geodesicity of the SGLSs are presented. Results for the totally umbilic screen generic lightlike submanifold with a QSNM connection are also established. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application, 3rd Edition)
19 pages, 292 KiB  
Article
Super Quasi-Einstein Warped Products Manifolds with Respect to Affine Connections
by Mohd Vasiulla, Mohabbat Ali, Meraj Ali Khan and Ibrahim Aldayel
Axioms 2025, 14(2), 110; https://doi.org/10.3390/axioms14020110 - 31 Jan 2025
Viewed by 608
Abstract
In this paper, we investigate warped products on super quasi-Einstein manifolds under affine connections. We explore their fundamental properties, establish conditions for their existence, and prove that these manifolds can also be nearly quasi-Einstein and pseudo quasi-Einstein. To illustrate, we provide examples in [...] Read more.
In this paper, we investigate warped products on super quasi-Einstein manifolds under affine connections. We explore their fundamental properties, establish conditions for their existence, and prove that these manifolds can also be nearly quasi-Einstein and pseudo quasi-Einstein. To illustrate, we provide examples in both Riemannian and Lorentzian geometries, confirming their existence. Finally, we construct and analyze an explicit example of a warped product on a super quasi-Einstein manifold with respect to affine connections. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application, 3rd Edition)
15 pages, 256 KiB  
Article
Extrinsic Geometry of a Riemannian Manifold and Ricci Solitons
by Ibrahim Al-Dayel and Sharief Deshmukh
Axioms 2025, 14(2), 95; https://doi.org/10.3390/axioms14020095 - 27 Jan 2025
Viewed by 498
Abstract
The object of this paper is to find a vector field ξ and a constant λ on an n-dimensional compact Riemannian manifold Mn,g such that we obtain the Ricci soliton Mn,g,ξ,λ. [...] Read more.
The object of this paper is to find a vector field ξ and a constant λ on an n-dimensional compact Riemannian manifold Mn,g such that we obtain the Ricci soliton Mn,g,ξ,λ. In order to achieve this objective, we choose an isometric embedding provided in the work of Kuiper and Nash in the Euclidean space Rm,g¯ and choose ξ as the tangential component of a constant unit vector on Rm and call it a Kuiper–Nash vector. If τ is the scalar curvature of the compact Riemannian manifold Mn,g with a Kuiper–Nash vector ξ, we show that if the integral of the function ξτ has a suitable lower bound containing a constant λ, then Mn,g,ξ,λ is a Ricci soliton; we call this a Kuiper–Nash Ricci soliton. We find a necessary and sufficient condition involving the scalar curvature τ under which a compact Kuiper–Nash Ricci soliton Mn,g,ξ,λ is a trivial soliton. Finally, we find a characterization of an n-dimensional compact trivial Kuiper–Nash Ricci soliton Mn,g,ξ,λ using an upper bound on the integral of divξ2 containing the scalar curvature τ. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application, 3rd Edition)
15 pages, 287 KiB  
Article
Sphere Theorems for σk-Einstein Manifolds
by Jingyang Zhong and Xinran Mu
Axioms 2025, 14(1), 68; https://doi.org/10.3390/axioms14010068 - 17 Jan 2025
Viewed by 471
Abstract
A problem that geometers have always been concerned with is when a closed manifold is isometric to a round sphere. A classical result shows that a closed locally conformally flat Einstein manifold is always isometric to a quotient of a round sphere. In [...] Read more.
A problem that geometers have always been concerned with is when a closed manifold is isometric to a round sphere. A classical result shows that a closed locally conformally flat Einstein manifold is always isometric to a quotient of a round sphere. In this note, we provide the definitions of σk-curvatures and σk-Einstein manifolds, and we show that a closed σk-Einstein manifold under certain pinching conditions of a Weyl curvature and Einstein curvature is isometric to a quotient of a round sphere. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application, 3rd Edition)
21 pages, 324 KiB  
Article
(Almost) Ricci Solitons in Lorentzian–Sasakian Hom-Lie Groups
by Esmaeil Peyghan, Leila Nourmohammadifar, Akram Ali and Ion Mihai
Axioms 2024, 13(10), 693; https://doi.org/10.3390/axioms13100693 - 4 Oct 2024
Viewed by 685
Abstract
We study Lorentzian contact and Lorentzian–Sasakian structures in Hom-Lie algebras. We find that the three-dimensional sl(2,R) and Heisenberg Lie algebras provide examples of such structures, respectively. Curvature tensor properties in Lorentzian–Sasakian Hom-Lie algebras are investigated. If v is [...] Read more.
We study Lorentzian contact and Lorentzian–Sasakian structures in Hom-Lie algebras. We find that the three-dimensional sl(2,R) and Heisenberg Lie algebras provide examples of such structures, respectively. Curvature tensor properties in Lorentzian–Sasakian Hom-Lie algebras are investigated. If v is a contact 1-form, conditions under which the Ricci curvature tensor is v-parallel are given. Ricci solitons for Lorentzian–Sasakian Hom-Lie algebras are also studied. It is shown that a Ricci soliton vector field ζ is conformal whenever the Lorentzian–Sasakian Hom-Lie algebra is Ricci semisymmetric. To illustrate the use of the theory, a two-parameter family of three-dimensional Lorentzian–Sasakian Hom-Lie algebras which are not Lie algebras is given and their Ricci solitons are computed. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application, 3rd Edition)
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