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Mathematics
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Recent Studies in Differential Geometry and Its Applications
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Recent Studies in Differential Geometry and Its Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "B: Geometry and Topology".

Deadline for manuscript submissions: 10 August 2025 | Viewed by 5935

Special Issue Editor

Dr. Hristo Manev

E-Mail Website
Guest Editor
Section Mathematics and IT, Department of Medical Physics and Biophysics, Faculty of Pharmacy, Medical University—Plovdiv, 15-A Vasil Aprilov Blvd., 4002 Plovdiv, Bulgaria
Interests: differential geometry; applications of mathematics; statistics; electronic education

Special Issue Information

Dear Colleagues,

An important fundamental branch in the field of mathematics is differential geometry. As is well known, differential geometry deals with the study of smooth manifolds, and it has numerous applications in various fields, including mathematics, physics, engineering, computer graphics, and robotics.

The present Special Issue is devoted to recent studies on all topics related to differential geometry and its applications.

Dr. Hristo Manev
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • differentiable manifold
  • (pseudo-)Riemannian metric
  • affine connection
  • soliton
  • vector field

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Published Papers (6 papers)

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Research

Jump to: Review

13 pages, 264 KiB  
Article
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 571
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  
Article
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 749
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)
11 pages, 288 KiB  
Article
Characterization of Bach and Cotton Tensors on a Class of Lorentzian Manifolds
by Yanlin Li, M. S. Siddesha, H. Aruna Kumara and M. M. Praveena
Mathematics 2024, 12(19), 3130; https://doi.org/10.3390/math12193130 - 7 Oct 2024
Cited by 8 | Viewed by 1074
Abstract
In this work, we aim to investigate the characteristics of the Bach and Cotton tensors on Lorentzian manifolds, particularly those admitting a semi-symmetric metric ω-connection. First, we prove that a Lorentzian manifold admitting a semi-symmetric metric ω-connection with a parallel Cotton [...] Read more.
In this work, we aim to investigate the characteristics of the Bach and Cotton tensors on Lorentzian manifolds, particularly those admitting a semi-symmetric metric ω-connection. First, we prove that a Lorentzian manifold admitting a semi-symmetric metric ω-connection with a parallel Cotton tensor is quasi-Einstein and Bach flat. Next, we show that any quasi-Einstein Lorentzian manifold admitting a semi-symmetric metric ω-connection is Bach flat. Full article
(This article belongs to the Special Issue Recent Studies in Differential Geometry and Its Applications)
9 pages, 261 KiB  
Article
Ricci–Bourguignon Almost Solitons with Special Potential on Sasaki-like Almost Contact Complex Riemannian Manifolds
by Mancho Manev
Mathematics 2024, 12(13), 2100; https://doi.org/10.3390/math12132100 - 4 Jul 2024
Cited by 1 | Viewed by 914
Abstract
Almost contact complex Riemannian manifolds, also known as almost contact B-metric manifolds, are equipped with a pair of pseudo-Riemannian metrics that are mutually associated with each other using the tensor structure. Here, we consider a special class of these manifolds, namely those of [...] Read more.
Almost contact complex Riemannian manifolds, also known as almost contact B-metric manifolds, are equipped with a pair of pseudo-Riemannian metrics that are mutually associated with each other using the tensor structure. Here, we consider a special class of these manifolds, namely those of the Sasaki-like type. They have an interesting geometric interpretation: the complex cone of such a manifold is a holomorphic complex Riemannian manifold (also called a Kähler–Norden manifold). The basic metric on the considered manifold is specialized here as a soliton, i.e., has an additional curvature property such that the metric is a self-similar solution to an intrinsic geometric flow. Almost solitons are more general objects than solitons because they use functions rather than constants as coefficients in the defining condition. A β-Ricci–Bourguignon-like almost soliton (β is a real constant) is defined using the pair of metrics. The introduced soliton is a generalization of some well-known (almost) solitons (such as those of Ricci, Schouten, and Einstein) which, in principle, arise from a single metric rather than a pair of metrics. The soliton potential is chosen to be pointwise collinear to the Reeb vector field, or the Lie derivative of any B-metric along the potential to be the same metric multiplied by a function. The resulting manifolds equipped with the introduced almost solitons are characterized geometrically. Suitable examples for both types of almost solitons are constructed, and the properties obtained in the theoretical part are confirmed. Full article
(This article belongs to the Special Issue Recent Studies in Differential Geometry and Its Applications)
18 pages, 293 KiB  
Article
Analyzing Curvature Properties and Geometric Solitons of the Twisted Sasaki Metric on the Tangent Bundle over a Statistical Manifold
by Lixu Yan, Yanlin Li, Lokman Bilen and Aydın Gezer
Mathematics 2024, 12(9), 1395; https://doi.org/10.3390/math12091395 - 2 May 2024
Cited by 1 | Viewed by 1294
Abstract
Let (M,∇,g) be a statistical manifold and TM be its tangent bundle endowed with a twisted Sasaki metric G. This paper serves two primary objectives. The first objective is to investigate the curvature properties of [...] Read more.
Let (M,∇,g) be a statistical manifold and TM be its tangent bundle endowed with a twisted Sasaki metric G. This paper serves two primary objectives. The first objective is to investigate the curvature properties of the tangent bundle TM. The second objective is to explore conformal vector fields and Ricci, Yamabe, and gradient Ricci–Yamabe solitons on the tangent bundle TM according to the twisted Sasaki metric G. Full article
(This article belongs to the Special Issue Recent Studies in Differential Geometry and Its Applications)

Review

Jump to: Research

24 pages, 395 KiB  
Review
Geometry of Weak Metric f-Manifolds: A Survey
by Vladimir Rovenski
Mathematics 2025, 13(4), 556; https://doi.org/10.3390/math13040556 - 8 Feb 2025
Viewed by 394
Abstract
The interest of geometers in f-structures is motivated by the study of the dynamics of contact foliations, as well as their applications in physics. A weak f-structure on a smooth manifold, introduced by the author and R. Wolak, generalizes K. Yano’s [...] Read more.
The interest of geometers in f-structures is motivated by the study of the dynamics of contact foliations, as well as their applications in physics. A weak f-structure on a smooth manifold, introduced by the author and R. Wolak, generalizes K. Yano’s f-structure. This generalization allows us to revisit classical theory and discover applications of Killing vector fields, totally geodesic foliations, Ricci-type solitons, and Einstein-type metrics. This article reviews the results regarding weak metric f-manifolds and their distinguished classes. Full article
(This article belongs to the Special Issue Recent Studies in Differential Geometry and Its Applications)
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