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Mathematics
Special Issues
New Trends in Differential Geometry and Geometric Analysis
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New Trends in Differential Geometry and Geometric Analysis

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

Deadline for manuscript submissions: 31 January 2026 | Viewed by 452

Special Issue Editors

Dr. Marija S. Najdanović

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Guest Editor
Faculty of Sciences and Mathematics, University of Priština in Kosovska Mitrovica, 38220 Kosovska Mitrovica, Serbia
Interests: differential geometry of curves and surfaces; infinitesimal bending; generalized Riemannian spaces; geometric knot theory; applications of geometry to natural processes
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Ljubica Velimirovic

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Guest Editor
Department of Mathematics, Faculty of Sciences and Mathematics, University of Niš, 18 000 Niš, Serbia
Interests: differential geometry; analytical geometry; foundations of geometry; descriptive geometry; geometry
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue aims to highlight recent developments and directions in differential geometry and geometric analysis, two fields that lie at the heart of many significant advances in mathematics and its applications. These areas have seen remarkable progress through the interplay of geometric intuition and analytical techniques, yielding deep insights into the structure and behavior of spaces and mappings.

We welcome contributions on a wide range of topics, including differential geometry of curves, surfaces and manifolds, Riemannian and complex geometry, spaces with non-symmetric affine connection, Minkowski spaces, dual spaces, shape and energy of geometric objects, geometric knot theory, geometric flows, geometric partial differential equations, variational methods in geometry, and applications to related fields such as topology and mathematical physics.

All related topics within the broader scope of differential geometry and geometric analysis are welcome for this Special Issue.

Dr. Marija S. Najdanović
Prof. Dr. Ljubica Velimirovic
Guest Editors

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. 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
  • infinitesimal deformations
  • curves and surfaces
  • manifolds
  • knots
  • shape and energy of geometric objects
  • Riemannian geometry and generalizations
  • minkowski spaces
  • dual spaces
  • geometric flows
  • geometric partial differential equations
  • minimal surfaces
  • variational methods
  • global analysis.

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Published Papers (1 paper)

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Research

19 pages, 301 KiB  
Article
Geometric and Structural Properties of Indefinite Kenmotsu Manifolds Admitting Eta-Ricci–Bourguignon Solitons
by Md Aquib, Oğuzhan Bahadır, Laltluangkima Chawngthu and Rajesh Kumar
Mathematics 2025, 13(12), 1965; https://doi.org/10.3390/math13121965 - 14 Jun 2025
Viewed by 300
Abstract
This paper undertakes a detailed study of η-Ricci–Bourguignon solitons on ϵ-Kenmotsu manifolds, with particular focus on three special types of Ricci tensors: Codazzi-type, cyclic parallel and cyclic η-recurrent tensors that support such solitonic structures. We derive key curvature conditions satisfying [...] Read more.
This paper undertakes a detailed study of η-Ricci–Bourguignon solitons on ϵ-Kenmotsu manifolds, with particular focus on three special types of Ricci tensors: Codazzi-type, cyclic parallel and cyclic η-recurrent tensors that support such solitonic structures. We derive key curvature conditions satisfying Ricci semi-symmetric (R·E=0), conharmonically Ricci semi-symmetric (C(ξ,βX)·E=0), ξ-projectively flat (P(βX,βY)ξ=0), projectively Ricci semi-symmetric (L·P=0) and W5-Ricci semi-symmetric (W(ξ,βY)·E=0), respectively, with the admittance of η-Ricci–Bourguignon solitons. This work further explores the role of torse-forming vector fields and provides a thorough characterization of ϕ-Ricci symmetric indefinite Kenmotsu manifolds admitting η-Ricci–Bourguignon solitons. Through in-depth analysis, we establish significant geometric constraints that govern the behavior of these manifolds. Finally, we construct explicit examples of indefinite Kenmotsu manifolds that satisfy the η-Ricci–Bourguignon solitons equation, thereby confirming their existence and highlighting their unique geometric properties. Moreover, these solitonic structures extend soliton theory to indefinite and physically meaningful settings, enhance the classification and structure of complex geometric manifolds by revealing how contact structures behave under advanced geometric flows and link the pure mathematical geometry to applied fields like general relativity. Furthermore, η-Ricci–Bourguignon solitons provide a unified framework that deepens our understanding of geometric evolution and structure-preserving transformations. Full article
(This article belongs to the Special Issue New Trends in Differential Geometry and Geometric Analysis)
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