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Axioms
Special Issues
Differential Geometry and Its Application
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Differential Geometry and Its Application

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

Deadline for manuscript submissions: closed (20 January 2023) | Viewed by 32828

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,

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 would 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 address this particular issue, we can consider the following non-exhaustive list:

Riemannian Spaces and generalizations, Kenmotsu manifolds, Kaehler manifolds, manifolds with non-symmetric linear connection, cosymplectic 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 the 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 (17 papers)

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Editorial

Jump to: Research

4 pages, 201 KiB  
Editorial
Differential Geometry and Its Application
by Mića S. Stanković
Axioms 2023, 12(9), 810; https://doi.org/10.3390/axioms12090810 - 23 Aug 2023
Viewed by 1459
Abstract
We have launched a Special Issue of Axioms which focuses on the generalization of Riemannian spaces and their mappings [...] Full article
(This article belongs to the Special Issue Differential Geometry and Its Application)

Research

Jump to: Editorial

11 pages, 267 KiB  
Article
On Bochner Flat Kähler B-Manifolds
by Cornelia-Livia Bejan, Galia Nakova and Adara M. Blaga
Axioms 2023, 12(4), 336; https://doi.org/10.3390/axioms12040336 - 30 Mar 2023
Cited by 2 | Viewed by 1558
Abstract
We obtain on a Kähler B-manifold (i.e., a Kähler manifold with a Norden metric) some corresponding results from the Kählerian and para-Kählerian context concerning the Bochner curvature. We prove that such a manifold is of constant totally real sectional curvatures if and only [...] Read more.
We obtain on a Kähler B-manifold (i.e., a Kähler manifold with a Norden metric) some corresponding results from the Kählerian and para-Kählerian context concerning the Bochner curvature. We prove that such a manifold is of constant totally real sectional curvatures if and only if it is a holomorphic Einstein, Bochner flat manifold. Moreover, we provide the necessary and sufficient conditions for a gradient Ricci soliton or a holomorphic η-Einstein Kähler manifold with a Norden metric to be Bochner flat. Finally, we show that a Kähler B-manifold is of quasi-constant totally real sectional curvatures if and only if it is a holomorphic η-Einstein, Bochner flat manifold. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application)
13 pages, 282 KiB  
Article
On r-Compactness in Topological and Bitopological Spaces
by Jamal Oudetallah, Rehab Alharbi and Iqbal M. Batiha
Axioms 2023, 12(2), 210; https://doi.org/10.3390/axioms12020210 - 16 Feb 2023
Cited by 9 | Viewed by 1478
Abstract
This paper defines the so-called pairwise r-compactness in topological and bitopological spaces. In particular, several inferred properties of the r-compact spaces and their connections with other topological and bitopological spaces are studied theoretically. As a result, several novel theorems of the [...] Read more.
This paper defines the so-called pairwise r-compactness in topological and bitopological spaces. In particular, several inferred properties of the r-compact spaces and their connections with other topological and bitopological spaces are studied theoretically. As a result, several novel theorems of the r-compact space are generalized on the pairwise r-compact space. The results established in this research paper are new in the field of topology. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application)
14 pages, 309 KiB  
Article
Certain Curvature Conditions on Kenmotsu Manifolds and 🟉-η-Ricci Solitons
by Halil İbrahim Yoldaş, Abdul Haseeb and Fatemah Mofarreh
Axioms 2023, 12(2), 140; https://doi.org/10.3390/axioms12020140 - 30 Jan 2023
Cited by 7 | Viewed by 1722
Abstract
The present paper deals with the investigations of a Kenmotsu manifold satisfying certain curvature conditions endowed with 🟉-η-Ricci solitons. First we find some necessary conditions for such a manifold to be φ-Einstein. Then, we study the notion of 🟉-η [...] Read more.
The present paper deals with the investigations of a Kenmotsu manifold satisfying certain curvature conditions endowed with 🟉-η-Ricci solitons. First we find some necessary conditions for such a manifold to be φ-Einstein. Then, we study the notion of 🟉-η-Ricci soliton on this manifold and prove some significant results related to this notion. Finally, we construct a nontrivial example of three-dimensional Kenmotsu manifolds to verify some of our results. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application)
10 pages, 288 KiB  
Article
A Superbundle Description of Differential K-Theory
by Jae Min Lee and Byungdo Park
Axioms 2023, 12(1), 82; https://doi.org/10.3390/axioms12010082 - 12 Jan 2023
Cited by 1 | Viewed by 1653
Abstract
We construct a model of differential K-theory using superbundles with a Z/2Z-graded connection and a differential form on the base manifold and prove that our model is isomorphic to the Freed–Lott–Klonoff model of differential K-theory. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application)
14 pages, 286 KiB  
Article
Soft Complete Continuity and Soft Strong Continuity in Soft Topological Spaces
by Samer Al Ghour
Axioms 2023, 12(1), 78; https://doi.org/10.3390/axioms12010078 - 12 Jan 2023
Cited by 6 | Viewed by 1637
Abstract
In this paper, we introduce soft complete continuity as a strong form of soft continuity and we introduce soft strong continuity as a strong form of soft complete continuity. Several characterizations, compositions, and restriction theorems are obtained. Moreover, several preservation theorems regarding soft [...] Read more.
In this paper, we introduce soft complete continuity as a strong form of soft continuity and we introduce soft strong continuity as a strong form of soft complete continuity. Several characterizations, compositions, and restriction theorems are obtained. Moreover, several preservation theorems regarding soft compactness, soft Lindelofness, soft connectedness, soft regularity, soft normality, soft almost regularity, soft mild normality, soft almost compactness, soft almost Lindelofness, soft near compactness, soft near Lindelofness, soft paracompactness, soft near paracompactness, soft almost paracompactness, and soft metacompactness are obtained. In addition to these, the study deals with the correlation between our new concepts in soft topology and their corresponding concepts in general topology; as a result, we show that soft complete continuity (resp. soft strong continuity) in soft topology is an extension of complete continuity (resp. strong continuity) in soft topology. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application)
10 pages, 1069 KiB  
Article
On a Surface Associated to the Catalan Triangle
by Marilena Jianu, Sever Achimescu, Leonard Dăuş, Ion Mierluş-Mazilu, Adela Mihai and Daniel Tudor
Axioms 2022, 11(12), 685; https://doi.org/10.3390/axioms11120685 - 30 Nov 2022
Cited by 1 | Viewed by 1409
Abstract
We define a surface that interpolates the ballot numbers in the Catalan triangle corresponding to every pair of nonnegative integers (except for the origin). We study the geometric properties of this surface and prove that it contains exactly five half-lines. The mean curvature [...] Read more.
We define a surface that interpolates the ballot numbers in the Catalan triangle corresponding to every pair of nonnegative integers (except for the origin). We study the geometric properties of this surface and prove that it contains exactly five half-lines. The mean curvature and the Gauss curvature of the surface are also calculated. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application)
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15 pages, 305 KiB  
Article
On h-Quasi-Hemi-Slant Riemannian Maps
by Mohd Bilal, Sushil Kumar, Rajendra Prasad, Abdul Haseeb and Sumeet Kumar
Axioms 2022, 11(11), 641; https://doi.org/10.3390/axioms11110641 - 14 Nov 2022
Cited by 1 | Viewed by 1512
Abstract
In the present article, we indroduce and study h-quasi-hemi-slant (in short, h-qhs) Riemannian maps and almost h-qhs Riemannian maps from almost quaternionic Hermitian manifolds to Riemannian manifolds. We investigate some fundamental results mainly on h-qhs Riemannian maps: the integrability [...] Read more.
In the present article, we indroduce and study h-quasi-hemi-slant (in short, h-qhs) Riemannian maps and almost h-qhs Riemannian maps from almost quaternionic Hermitian manifolds to Riemannian manifolds. We investigate some fundamental results mainly on h-qhs Riemannian maps: the integrability of distributions, geometry of foliations, the condition for such maps to be totally geodesic, etc. At the end of this article, we give two non-trivial examples of this notion. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application)
13 pages, 802 KiB  
Article
Soft Regular Generalized ω-Closed Sets and Soft ω-T1/2 Spaces
by Samer Al Ghour
Axioms 2022, 11(10), 529; https://doi.org/10.3390/axioms11100529 - 3 Oct 2022
Cited by 2 | Viewed by 1486
Abstract
Soft rgω-closed sets are introduced as a new class of soft sets that strictly contain the classes of soft rg-closed sets and soft gω-closed sets. Furthermore, the behavior of soft rgω-closed sets with [...] Read more.
Soft rgω-closed sets are introduced as a new class of soft sets that strictly contain the classes of soft rg-closed sets and soft gω-closed sets. Furthermore, the behavior of soft rgω-closed sets with respect to soft unions, soft intersections, and soft subspaces, as well as induced soft topologies are investigated. Moreover, soft ω-T1/2 spaces which is a weaker form soft T1/2 spaces is defined and investigated. In addition to these, the characterizations of soft rg-T1/2 spaces and soft rgω-T1/2 spaces are discussed. The work also looks at the relationship between our novel notions in soft topological spaces and their analogs in topological spaces. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application)
17 pages, 316 KiB  
Article
A Study of Clairaut Semi-Invariant Riemannian Maps from Cosymplectic Manifolds
by Yanlin Li, Rajendra Prasad, Abdul Haseeb, Sushil Kumar and Sumeet Kumar
Axioms 2022, 11(10), 503; https://doi.org/10.3390/axioms11100503 - 26 Sep 2022
Cited by 19 | Viewed by 1963
Abstract
In the present note, we characterize Clairaut semi-invariant Riemannian maps from cosymplectic manifolds to Riemannian manifolds. Moreover, we provide a nontrivial example of such a Riemannian map. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application)
17 pages, 326 KiB  
Article
Classification of Surfaces of Coordinate Finite Type in the Lorentz–Minkowski 3-Space
by Hassan Al-Zoubi, Alev Kelleci Akbay, Tareq Hamadneh and Mutaz Al-Sabbagh
Axioms 2022, 11(7), 326; https://doi.org/10.3390/axioms11070326 - 4 Jul 2022
Cited by 7 | Viewed by 1700
Abstract
In this paper, we define surfaces of revolution without parabolic points in three-dimensional Lorentz–Minkowski space. Then, we classify this class of surfaces under the condition ΔIIIx=Ax, where ΔIII is the Laplace operator [...] Read more.
In this paper, we define surfaces of revolution without parabolic points in three-dimensional Lorentz–Minkowski space. Then, we classify this class of surfaces under the condition ΔIIIx=Ax, where ΔIII is the Laplace operator regarding the third fundamental form, and A is a real square matrix of order 3. We prove that such surfaces are either catenoids or surfaces of Enneper, or pseudo spheres or hyperbolic spaces centered at the origin. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application)
16 pages, 319 KiB  
Article
Improved Chen’s Inequalities for Submanifolds of Generalized Sasakian-Space-Forms
by Yanlin Li, Mohan Khatri, Jay Prakash Singh and Sudhakar K. Chaubey
Axioms 2022, 11(7), 324; https://doi.org/10.3390/axioms11070324 - 1 Jul 2022
Cited by 22 | Viewed by 2007
Abstract
In this article, we derive Chen’s inequalities involving Chen’s δ-invariant δM, Riemannian invariant δ(m1,⋯,mk), Ricci curvature, Riemannian invariant Θk(2≤k≤m), the scalar [...] Read more.
In this article, we derive Chen’s inequalities involving Chen’s δ-invariant δM, Riemannian invariant δ(m1,⋯,mk), Ricci curvature, Riemannian invariant Θk(2≤k≤m), the scalar curvature and the squared of the mean curvature for submanifolds of generalized Sasakian-space-forms endowed with a quarter-symmetric connection. As an application of the obtain inequality, we first derived the Chen inequality for the bi-slant submanifold of generalized Sasakian-space-forms. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application)
15 pages, 315 KiB  
Article
Two Invariants for Geometric Mappings
by Nenad O. Vesić, Vladislava M. Milenković and Mića S. Stanković
Axioms 2022, 11(5), 239; https://doi.org/10.3390/axioms11050239 - 20 May 2022
Cited by 2 | Viewed by 1782
Abstract
Two invariants for mappings of affine connection spaces with a special form of deformation tensors are obtained in this paper. We used the methodology of Vesić to obtain the form of these invariants. At the end of this paper, we used these forms [...] Read more.
Two invariants for mappings of affine connection spaces with a special form of deformation tensors are obtained in this paper. We used the methodology of Vesić to obtain the form of these invariants. At the end of this paper, we used these forms to obtain two invariants for third-type almost-geodesic mappings of symmetric affine connection. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application)
13 pages, 289 KiB  
Article
Soft Rω-Open Sets and the Soft Topology of Soft δω-Open Sets
by Samer Al Ghour
Axioms 2022, 11(4), 177; https://doi.org/10.3390/axioms11040177 - 15 Apr 2022
Cited by 8 | Viewed by 2092
Abstract
The author devotes this paper to defining a new class of soft open sets, namely soft Rω-open sets, and investigating their main features. With the help of examples, we show that the class of soft Rω-open sets lies strictly [...] Read more.
The author devotes this paper to defining a new class of soft open sets, namely soft Rω-open sets, and investigating their main features. With the help of examples, we show that the class of soft Rω-open sets lies strictly between the classes of soft regular open sets and soft open sets. We show that soft Rω-open subsets of a soft locally countable soft topological space coincide with the soft open sets. Moreover, we show that soft Rω-open subsets of a soft anti-locally countable coincide with the soft regular open sets. Moreover, we show that the class of soft Rω-open sets is closed under finite soft intersection, and as a conclusion, we show that this class forms a soft base for some soft topology. In addition, we define the soft δω-closure operator as a new operator in soft topological spaces. Moreover, via the soft δω-closure operator, we introduce soft δω-open sets as a new class of soft open sets which form a soft topology. Moreover, we study the correspondence between soft δω-open in soft topological spaces and δω-open in topological spaces. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application)
12 pages, 297 KiB  
Article
Pythagorean Isoparametric Hypersurfaces in Riemannian and Lorentzian Space Forms
by Muhittin Evren Aydın, Adela Mihai and Cihan Özgür
Axioms 2022, 11(2), 59; https://doi.org/10.3390/axioms11020059 - 30 Jan 2022
Cited by 2 | Viewed by 2453
Abstract
We introduce the notion of a Pythagorean hypersurface immersed into an n+1-dimensional pseudo-Riemannian space form of constant sectional curvature c∈−1,0,1. By using this definition, we prove in Riemannian setting that if an [...] Read more.
We introduce the notion of a Pythagorean hypersurface immersed into an n+1-dimensional pseudo-Riemannian space form of constant sectional curvature c∈−1,0,1. By using this definition, we prove in Riemannian setting that if an isoparametric hypersurface is Pythagorean, then it is totally umbilical with sectional curvature φ+c, where φ is the Golden Ratio. We also extend this result to Lorentzian ambient space, observing the existence of a non totally umbilical model. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application)
6 pages, 351 KiB  
Article
A Model of Directed Graph Cofiber
by Zachary McGuirk and Byungdo Park
Axioms 2022, 11(1), 32; https://doi.org/10.3390/axioms11010032 - 16 Jan 2022
Cited by 1 | Viewed by 2332
Abstract
In the homotopy theory of spaces, the image of a continuous map is contractible to a point in its cofiber. This property does not apply when we discretize spaces and continuous maps to directed graphs and their morphisms. In this paper, we give [...] Read more.
In the homotopy theory of spaces, the image of a continuous map is contractible to a point in its cofiber. This property does not apply when we discretize spaces and continuous maps to directed graphs and their morphisms. In this paper, we give a construction of a cofiber of a directed graph map whose image is contractible in the cofiber. Our work reveals that a category-theoretically correct construction in continuous setup is no longer correct when it is discretized and hence leads to look at canonical constructions in category theory in a different perspective. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application)
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10 pages, 286 KiB  
Article
A Generalized Bochner Technique and Its Application to the Study of Conformal Mappings
by Vladimir Rovenski, Sergey Stepanov and Irina Tsyganok
Axioms 2021, 10(4), 333; https://doi.org/10.3390/axioms10040333 - 5 Dec 2021
Cited by 2 | Viewed by 2517
Abstract
This article is devoted to geometrical aspects of conformal mappings of complete Riemannian and Kählerian manifolds and uses the Bochner technique, one of the oldest and most important techniques in modern differential geometry. A feature of this article is that the results presented [...] Read more.
This article is devoted to geometrical aspects of conformal mappings of complete Riemannian and Kählerian manifolds and uses the Bochner technique, one of the oldest and most important techniques in modern differential geometry. A feature of this article is that the results presented here are easily obtained using a generalized version of the Bochner technique due to theorems on the connection between the geometry of a complete Riemannian manifold and the global behavior of its subharmonic, superharmonic, and convex functions. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application)
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