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Mathematics
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Differential Geometry, Geometric Analysis and Their Related Applications, 2nd Edition
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Differential Geometry, Geometric Analysis and Their Related Applications, 2nd Edition

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

Deadline for manuscript submissions: 31 December 2026 | Viewed by 1826

Special Issue Editor

Prof. Dr. Mića S. Stanković

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Sciences and Mathematics, University of Nis, Niš, Serbia
Interests: differential geometry; geodesic mappings; infinitesimal deformations of curves and surfaces in R3; tensor calculus; spaces with non symmetric affine connection; generalized Riemannian spaces; computer graphics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

As an important branch of mathematics, differential geometry provides a mathematical framework for understanding the geometric structures and properties of spaces. Differential geometry encompasses a wide range of topics and has applications in various areas of mathematics, physics, engineering, and computer graphics, among others. This Special Issue, as a follow-up of the previous edition, is devoted to novel research on differential geometry, geometric analysis, and their wide-ranging applications. The topics covered in this Special Issue include, but are not limited to, the following:

  1. Differential Geometry: Riemannian geometry, manifolds, Finsler geometry, symplectic geometry, contact geometry, complex and Kähler geometry, geodesic mappings, Minkowski spaces, almost geodesic mappings, etc.
  2. Geometric Analysis: minimal surfaces, geometric flows, geometric measure theory, geometric functional theory, geometric inequalities, such as the isoperimetric inequality, Sobolev inequalities, and the Minkowski inequality.
  3. Geometric Methods in Image Processing and Computer Vision: topics such as geometric transformations, shape analysis, geometric modeling, and geometric methods for image registration and segmentation.
  4. Applications in Engineering and Applied Sciences.

All the related topics on the areas of differential geometry and geometric analysis are of interest for this Special Issue.

Prof. Dr. Mića S. Stanković
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-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

  • differential geometry
  • geometric analysis
  • manifolds
  • Finsler geometry
  • symplectic geometry
  • contact geometry
  • complex and Kähler geometry
  • geodesic mappings
  • Minkowski spaces
  • geometric inequalities
  • geometric models
  • infinitesimal deformations of curves and surfaces
  • tensor calculus
  • spaces with non-symmetric affine connection
  • generalized Riemannian spaces

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Related Special Issue

Published Papers (4 papers)

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Research

19 pages, 309 KB  
Article
Geometry of Riemannian Maps from Generic Submanifolds of Kähler Manifolds
by Tanveer Fatima and Ibrahim Al-Dayel
Mathematics 2026, 14(4), 672; https://doi.org/10.3390/math14040672 - 13 Feb 2026
Abstract
This paper extends the theory of Riemannian maps to the setting of generic submanifolds of Kähler manifolds. We introduce the notion of holomorphic Riemannian maps from generic submanifolds and establish fundamental relations between the geometric structures involved. Our main results include a characterization [...] Read more.
This paper extends the theory of Riemannian maps to the setting of generic submanifolds of Kähler manifolds. We introduce the notion of holomorphic Riemannian maps from generic submanifolds and establish fundamental relations between the geometric structures involved. Our main results include a characterization of when the image distribution inherits a Kähler structure, a harmonicity criterion for such maps, and a relation between holomorphic sectional curvatures. The theory developed here generalizes previous work on CR-submanifolds while demonstrating new phenomena specific to the generic case. Several explicit examples illustrate the non-trivial nature of our results. Full article
(This article belongs to the Special Issue Differential Geometry, Geometric Analysis and Their Related Applications, 2nd Edition)
15 pages, 290 KB  
Article
Rigidity and Conformal Characterizations of Noncompact Gradient Schouten Solitons
by Ali H. Alkhaldi, Fatemah Mofarreh, Huda M. Alshanbari and Akram Ali
Mathematics 2026, 14(3), 562; https://doi.org/10.3390/math14030562 - 4 Feb 2026
Viewed by 157
Abstract
This paper studies the conformal geometry of complete gradient Schouten solitons (GSSs) admitting closed conformal vector fields (CVFs). We establish rigidity and characterization results for nonparallel, homothetic closed CVFs under the assumption that the gradient of the scalar curvature is parallel to the [...] Read more.
This paper studies the conformal geometry of complete gradient Schouten solitons (GSSs) admitting closed conformal vector fields (CVFs). We establish rigidity and characterization results for nonparallel, homothetic closed CVFs under the assumption that the gradient of the scalar curvature is parallel to the CVF. It is shown that such manifolds are isometric to Euclidean space. Moreover, complete noncompact GSSs with constant scalar curvature are locally conformally flat in dimension four and have harmonic Weyl curvature in higher dimensions. Finally, we prove that these manifolds are totally umbilical if and only if their scalar curvature is constant, and they form warped products with space forms. Full article
(This article belongs to the Special Issue Differential Geometry, Geometric Analysis and Their Related Applications, 2nd Edition)
14 pages, 3046 KB  
Article
Parallel Hypersurfaces in 𝔼4 and Their Applications to Rotational Hypersurfaces
by Sezgin Büyükkütük, Ilim Kişi, Günay Öztürk and Emre Kişi
Mathematics 2025, 13(22), 3684; https://doi.org/10.3390/math13223684 - 17 Nov 2025
Viewed by 446
Abstract
This study explores parallel hypersurfaces in four-dimensional Euclidean space E4, deriving explicit expressions for their Gaussian and mean curvatures in terms of the curvature functions of the base hypersurface. We identify conditions under which these parallel hypersurfaces are flat or minimal. [...] Read more.
This study explores parallel hypersurfaces in four-dimensional Euclidean space E4, deriving explicit expressions for their Gaussian and mean curvatures in terms of the curvature functions of the base hypersurface. We identify conditions under which these parallel hypersurfaces are flat or minimal. The theory is applied to several key hypersurfaces, including rotational hypersurfaces, hyperspheres, catenoidal hypersurfaces, and helicoidal hypersurfaces, with detailed curvature computations and visualizations. These results not only extend classical curvature relations into higher-dimensional spaces but also offer valuable insights into curvature transformations, with practical applications in both theoretical and computational geometry. Full article
(This article belongs to the Special Issue Differential Geometry, Geometric Analysis and Their Related Applications, 2nd Edition)
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9 pages, 267 KB  
Article
Laplacian Conditions and Sphericity of Hypersurfaces in the Nearly Kähler 6-Sphere
by Ibrahim Al-Dayel
Mathematics 2025, 13(16), 2673; https://doi.org/10.3390/math13162673 - 20 Aug 2025
Viewed by 685
Abstract
In this paper, we investigate hypersurfaces in the nearly Kähler 6-sphere S6 and establish several foundational results. In particular, under certain conditions of the function ξ(f)=g(∇f,ξ), we demonstrate that a [...] Read more.
In this paper, we investigate hypersurfaces in the nearly Kähler 6-sphere S6 and establish several foundational results. In particular, under certain conditions of the function ξ(f)=g(∇f,ξ), we demonstrate that a hypersurface M of S6 must be a sphere. Here, f∈C∞(M) is a smooth vector field, ξ=−JN denotes the characteristic vector field, J is the almost complex structure on S6, and N is the unit vector field normal to the hypersurface. We also support our results with illustrative examples. Full article
(This article belongs to the Special Issue Differential Geometry, Geometric Analysis and Their Related Applications, 2nd Edition)
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