New Research on Differential Geometry and Its Applications

A Special Issue of Axioms (ISSN 2075-1680) belonging to the section "Geometry and Topology".

Deadline for manuscript submissions: 30 October 2026 | Viewed by 791

Editors


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Guest Editor
Mathematical Institute, Serbian Academy of Sciences and Arts, 11000 Belgrade, Serbia
Interests: differential geometry of mappings; generalized Riemannian spaces and generalized affine connection spaces applied in physics; applications of differential geometry in multi-criteria decision making
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
Instituto de Matemática Interdisciplinar, Departamento de Geometría y Topología, Universidad Complutense de Madrid, Plaza de Ciencias 3, E-28040 Madrid, Spain
Interests: real and complex lie algebras and groups; differential forms and distribution theory; contractions and deformations; Casimir invariants; symmetries in physics; representation theory; lie group analysis of differential equations; Lagrangian and Hamiltonian formalism in classical mechanics; integrable and superintegrable systems; symmetry-conditioned perturbation theory; inverse problems in dynamics; supersymmetry
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Differential geometry has been applied in mechanics and cosmology. A paper that generalized the MCDM method in the sense of differential geometry was published in 2023 [1]. In light of this, this Special Issue will addresses the following topics: 1. theoretical differential geometry; 2. Riemannian spaces and cosmology; 3. graphical data analysis in quantum mechanics; and 4. differential geometry-based MCDM methods and applications. In part 1, authors should present novel results obtained with respect to tensor calculus. In part 2, novel computations in cosmology should be offered. In part 3, the application of quantum mechanics in chemistry covered by different graphical analyses should be presented. The aim of this Special Issue is to provide an overview of recent results that provide scope for further novel investigations into various areas of applied mathematics.

Reference

1. Simjanović, et al., A Novel Fuzzy Analytic Hierarchy Process, Filomat, Vol. 37, No. 11 (2023)

Dr. Nenad O. Vesić
Dr. Rutwig Campoamor-Stursberg
Guest Editors

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Keywords

  • tensor calculus
  • affine connection
  • metric tensor
  • inner product
  • curvature tensor
  • invariants
  • cosmological models
  • energy levels
  • fuzzy numbers and MCDM methods
  • graphical analysis

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Published Papers (1 paper)

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Research

24 pages, 382 KB  
Article
On (m¯,m)-Conformal Mappings and Their Geodesic Extension
by Nenad Vesić, Ivana Djurišić and Dušan Simjanović
Axioms 2026, 15(6), 446; https://doi.org/10.3390/axioms15060446 - 15 Jun 2026
Viewed by 352
Abstract
Many geometrical models have been created and applied in different subjects within the sciences, such as physics, astronomy, and biology. This paper presents a generalization of the recently defined (m¯,m)-conformal mappings of Riemannian spaces. In this article, [...] Read more.
Many geometrical models have been created and applied in different subjects within the sciences, such as physics, astronomy, and biology. This paper presents a generalization of the recently defined (m¯,m)-conformal mappings of Riemannian spaces. In this article, the affine connections of Riemannian spaces and symmetric affine connection spaces are combined. In this way, the characteristics of structures without external effects (Riemannian spaces) and with external effects (symmetric affine connection spaces) are geometrized. The main contributions of this research are as follows: (1) invariants of (m¯,m)-conformal mappings of Riemannian spaces (review) and geodesic mappings of symmetric affine connection spaces (review); (2) actions and variational calculi with respect to some invariants obtained in (1); (3) generalized Einstein’s equations with respect to the analyzed transformations with clear reductions to standard ones. Full article
(This article belongs to the Special Issue New Research on Differential Geometry and Its Applications)
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