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Advances in Differential Geometry and Its Applications, 2nd Edition
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Advances in Differential Geometry and Its 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 4309

Special Issue Editor

Dr. Stéphane Puechmorel

E-Mail Website
Guest Editor
Laboratoire de Mathématiques Appliquées, Ecole Nationale de l'Aviation Civile, 7 Av. Edouard Belin, 31400 Toulouse, France
Interests: information geometry; dual connections; gauge structures; foliations; differential geometry applied to machine learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Differential geometry is a wide and active research field in mathematics that has recently received increasing interest from statistics and machine learning. Information geometry, manifold learning, and data manifolds are examples of successful differential geometry uses.

This Special Issue welcomes papers presenting new theoretical results in various areas of differential geometry, as well as applications-oriented articles, and aims at a balance between both aspects. Review articles will also be considered.

Dr. Stéphane Puechmorel
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

  • Riemannian geometry
  • symplectic geometry
  • contact geometry
  • information geometry
  • gauge theory
  • Lie groups and Lie algebras
  • applications to machine learning
  • applications to data analysis

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Related Special Issue

Published Papers (5 papers)

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Research

20 pages, 322 KB  
Article
Characterizations of Transversal Lightlike Submanifolds in Indefinite Golden Statistical Geometry
by Md Aquib
Mathematics 2026, 14(4), 654; https://doi.org/10.3390/math14040654 - 12 Feb 2026
Viewed by 319
Abstract
We investigate transversal and radical transversal lightlike submanifolds (TLSs) of indefinite golden statistical manifolds (IGSMs). Using the dual affine connections associated with statistical structures, we obtain decomposition formulas and derive necessary and sufficient conditions for the integrability of the radical, screen, and lightlike [...] Read more.
We investigate transversal and radical transversal lightlike submanifolds (TLSs) of indefinite golden statistical manifolds (IGSMs). Using the dual affine connections associated with statistical structures, we obtain decomposition formulas and derive necessary and sufficient conditions for the integrability of the radical, screen, and lightlike transversal distributions. Criteria for totally geodesic foliations and local product structures are established. Explicit examples are provided to illustrate the theory. These results extend lightlike submanifold geometry to the golden statistical setting. Full article
(This article belongs to the Special Issue Advances in Differential Geometry and Its Applications, 2nd Edition)
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16 pages, 275 KB  
Article
Basic Inequalities for Submanifolds of Conformal Kenmotsu Manifolds
by Qiming Zhao, Mohamd Saleem Lone, Mehraj Ahmad Lone, Idrees Fayaz Harry and Yongqiao Wang
Mathematics 2026, 14(2), 339; https://doi.org/10.3390/math14020339 - 19 Jan 2026
Viewed by 345
Abstract
In this paper, we have established some basic inequalities for the submanifolds of conformal Kenmotsu manifolds. As an application, we have also derived the same inequalities for the θ-slant submanifolds of conformal Kenmotsu manifolds. Full article
(This article belongs to the Special Issue Advances in Differential Geometry and Its Applications, 2nd Edition)
25 pages, 361 KB  
Article
Killing and 2-Killing 1-Forms on Poisson Doubly Warped Product Manifolds
by Bang-Yen Chen, Majid Ali Choudhary, Foued Aloui and Ibrahim Al-Dayel
Mathematics 2026, 14(2), 301; https://doi.org/10.3390/math14020301 - 14 Jan 2026
Cited by 1 | Viewed by 411
Abstract
In this paper we investigate Killing and 2-Killing 1-forms on a Poisson doubly warped product manifold (PDWPM). We establish a connection between the property of 1-form on a PDWPM and its components on the factor manifolds to be Killing or 2-Killing. [...] Read more.
In this paper we investigate Killing and 2-Killing 1-forms on a Poisson doubly warped product manifold (PDWPM). We establish a connection between the property of 1-form on a PDWPM and its components on the factor manifolds to be Killing or 2-Killing. We also demonstrate that a Killing 1-form on a PDWPM generates a contravariant Ricci soliton factor manifold if and only if it is a contravariant Einstein manifold. Additionally, we provide necessary and sufficient conditions for a PDWPM to be a Poisson singly warped product manifold (PSWPM). Finally, we present examples of Killing and 2-Killing 1-forms on PDWPMs with one-dimensional, and two-dimensional base spaces. Full article
(This article belongs to the Special Issue Advances in Differential Geometry and Its Applications, 2nd Edition)
13 pages, 286 KB  
Article
Nonexistence of Homogeneous Levi-Flat Hypersurfaces in CP2
by Abdel Rahman Al-Abdallah
Mathematics 2025, 13(17), 2742; https://doi.org/10.3390/math13172742 - 26 Aug 2025
Viewed by 944
Abstract
We investigate the longstanding question of whether compact Levi-flat hypersurfaces exist in the complex projective plane CP2. While the nonexistence of closed real-analytic Levi-flat hypersurfaces in CPn for n>2 is well known, the case n=2 remains [...] Read more.
We investigate the longstanding question of whether compact Levi-flat hypersurfaces exist in the complex projective plane CP2. While the nonexistence of closed real-analytic Levi-flat hypersurfaces in CPn for n>2 is well known, the case n=2 remains open. By combining techniques from the classification of homogeneous CR-manifolds with projective foliation geometry, we prove that no homogeneous Levi-flat hypersurfaces exist in CP2, thus partially resolving the problem under natural symmetry assumptions. Full article
(This article belongs to the Special Issue Advances in Differential Geometry and Its Applications, 2nd Edition)
15 pages, 294 KB  
Article
On Convergence of Toeplitz Quantization of the Sphere
by Yanlin Li, Mohamed Lemine H. Bouleryah and Akram Ali
Mathematics 2024, 12(22), 3565; https://doi.org/10.3390/math12223565 - 14 Nov 2024
Cited by 8 | Viewed by 1279
Abstract
In this paper, we give an explicit expression of the Toeplitz quantization of a C∞ smooth function on the sphere and show that the sequence of spectra of Toeplitz quantization of the function determines its decreasing rearrangement. We also use Toeplitz quantization [...] Read more.
In this paper, we give an explicit expression of the Toeplitz quantization of a C∞ smooth function on the sphere and show that the sequence of spectra of Toeplitz quantization of the function determines its decreasing rearrangement. We also use Toeplitz quantization to prove a version of Szegö’s Theorem. Full article
(This article belongs to the Special Issue Advances in Differential Geometry and Its Applications, 2nd Edition)
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