Advances in Differential Geometry and Mathematical Physics, 2nd Edition

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: 31 December 2026 | Viewed by 1273

Special Issue Editor


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Guest Editor
Royal Norwegian Naval Academy, Norwegian Defense University College, 5165 Bergen, Norway
Interests: alternative gravity theories; Cartan invariants; pseudo-Riemannian geometry; teleparallel geometry; classification of manifolds
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

I am acting as the Guest Editor for a Special Issue on advances in differential geometry and mathematical physics in MDPI’s journal Axioms. Our intention with this Special Issue is to focus on new and interesting applications of differential geometry that are inspired by general relativity, its modifications, and alternative gravity theories.

In particular, we would like to provide an opportunity for scholars to present recent developments in mathematical physics that incorporate geometries beyond curvature-based Lorentzian geometries. This Special Issue will address the following non-exhaustive list of topics:

  • Symmetry methods.
  • Conformal symmetries.
  • The invariants associated with geometries.
  • The mathematical aspects of solutions to particular gravity theories.
  • Applications of pseudo-Riemannian geometries, teleparallel geometries, symmetric teleparallel geometries, Einstein–Cartan geometries, Finsler geometries, or Carrollian geometries to mathematical physics.

In addition to the above, any topic that relates to the application of differential geometry to mathematical physics is welcome.

We hope that this Special Issue will be attractive to experts in the field of mathematical physics who are exploring new ways to apply differential geometry to the problems they encounter. We encourage you to submit your current research or reviews to this Special Issue.

Dr. David D. McNutt
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. 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

  • pseudo-Riemannian geometry
  • teleparallel geometry
  • Riemann–Cartan geometry
  • symmetries
  • invariants
  • black holes
  • conformal symmetries
  • alternative theories of gravity

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Published Papers (3 papers)

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Research

21 pages, 351 KB  
Article
Geometry of Ricci–Bourguignon Solitons on Mixed Doubly Sequential Warped Products: Existence, Classification, and Cosmological Implications
by Ayman Elsharkawy, Anis Ben Ghorbal, Majdah Mohammed Badr and Uday Chand De
Axioms 2026, 15(5), 318; https://doi.org/10.3390/axioms15050318 - 28 Apr 2026
Viewed by 235
Abstract
We investigate Ricci–Bourguignon solitons on mixed doubly sequential warped product manifolds. Necessary and sufficient conditions for the existence of such solitons are established, and their implications for Einstein manifolds are analyzed. This work extends previous results on warped product manifolds to the more [...] Read more.
We investigate Ricci–Bourguignon solitons on mixed doubly sequential warped product manifolds. Necessary and sufficient conditions for the existence of such solitons are established, and their implications for Einstein manifolds are analyzed. This work extends previous results on warped product manifolds to the more complex case of mixed doubly sequential warped products. We derive explicit formulas for Ricci tensor components, establish conditions for Einstein metrics, and study gradient solitons and conformal vector fields. Our classification theorems reveal fundamental separability constraints on the warping functions. Applications to cosmological models and black hole solutions demonstrate the physical relevance of these results. Full article
15 pages, 265 KB  
Article
Riemann Solitons on a Spacetime with the Spatially Homogeneous Rotating Metric
by Majid Ali Choudhary, Foued Aloui and Ibrahim Al-Dayel
Axioms 2026, 15(4), 248; https://doi.org/10.3390/axioms15040248 - 26 Mar 2026
Viewed by 371
Abstract
This manuscript presents a comprehensive taxonomy of Riemann solitons within the framework of a spacetime manifold endowed with a metric exhibiting both spatial homogeneity and rotational characteristics. Furthermore, we undertake an analysis to determine the geometric nature of these solitons by establishing their [...] Read more.
This manuscript presents a comprehensive taxonomy of Riemann solitons within the framework of a spacetime manifold endowed with a metric exhibiting both spatial homogeneity and rotational characteristics. Furthermore, we undertake an analysis to determine the geometric nature of these solitons by establishing their correspondence to Killing vector fields, Ricci collineation vector fields, and gradient vector fields. Full article
13 pages, 280 KB  
Article
Curvature Pinching Conditions in Quaternionic Manifolds Under Quarter-Symmetric Metric Connections
by Md Aquib and Ibrahim Al-Dayel
Axioms 2026, 15(3), 164; https://doi.org/10.3390/axioms15030164 - 27 Feb 2026
Viewed by 278
Abstract
This work presents a pair of sharp geometric inequalities that connect the normalized scalar curvature with the generalized normalized δ-Casorati curvature for θ-slant submanifolds immersed in quaternionic space forms endowed with a quarter-symmetric metric connection (QSMC). Alongside establishing these estimates, we [...] Read more.
This work presents a pair of sharp geometric inequalities that connect the normalized scalar curvature with the generalized normalized δ-Casorati curvature for θ-slant submanifolds immersed in quaternionic space forms endowed with a quarter-symmetric metric connection (QSMC). Alongside establishing these estimates, we rigorously describe the geometric conditions under which equality is achieved. The results not only generalize prior findings related to Casorati curvature but also offer new insights into the extrinsic geometry of submanifolds under non-standard connections. To conclude, we propose several open problems that invite further exploration in this direction. Full article
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