Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.0
2.3
Journals
Mathematics
Special Issues
Differential Geometric Structures and Their Applications
share announcement

Differential Geometric Structures and Their Applications

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

Deadline for manuscript submissions: 31 August 2025 | Viewed by 3286

Special Issue Editor

Prof. Dr. Vladimir Rovenski

E-Mail Website
Guest Editor
Department of Mathematics, University of Haifa, Mount Carmel, 3498838 Haifa, Israel
Interests: smooth manifold; submanifold; foliation; metric structure; curvature; tensor
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The Special Issue is devoted to Riemannian manifolds and submanifolds equipped with various additional geometric structures, such as foliation, distribution, almost product, almost contact, and complex structures. The topics covered in this Special Issue include the following: local and global differential geometry, curvature and topology of Riemannian manifolds and submanifolds (regular and with singularities); geometric inequalities related to extrinsic to intrinsic curvature invariants; variational problems for curvature functionals; almost contact (Sasakian, Kenmotsu, cosymplectic, etc.) structures and Ricci-type solitons; manifolds with density; etc.

Prof. Dr. Vladimir Rovenski
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 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

  • Riemannian manifold
  • submanifold
  • foliation
  • almost product manifold
  • almost contact manifold
  • second fundamental form
  • curvature
  • variation
  • Ricci-type soliton
  • Einstein-type metric
  • geometric analysis
  • geometric flow

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

23 pages, 1537 KiB  
Article
CR-Selfdual Cubic Curves
by Mircea Crasmareanu, Cristina-Liliana Pripoae and Gabriel-Teodor Pripoae
Mathematics 2025, 13(2), 317; https://doi.org/10.3390/math13020317 - 19 Jan 2025
Cited by 1 | Viewed by 539
Abstract
We introduce a special class of cubic curves whose defining parameter satisfies a linear or quadratic equation provided by the values of a cross ratio. There are only seven such cubics and several properties of the real cubics in this class (some of [...] Read more.
We introduce a special class of cubic curves whose defining parameter satisfies a linear or quadratic equation provided by the values of a cross ratio. There are only seven such cubics and several properties of the real cubics in this class (some of them being elliptic curves) are discussed. Using the Möbius transformation, we extend this self-duality and obtain new families of remarkable complex cubics. In addition, we study (from the differential geometric viewpoint) the surface parameterized by all real cubic curves and we derive its curvature functions. As a by-product, we find a new classification of real Möbius transformations and some estimates for the number of vertices of real cubic curves. Full article
(This article belongs to the Special Issue Differential Geometric Structures and Their Applications)
►▼ Show Figures

Figure 1

18 pages, 318 KiB  
Article
Spinor Equations of Smarandache Curves in E3
by Zeynep İsabeyoǧlu, Tülay Erişir and Ayşe Zeynep Azak
Mathematics 2024, 12(24), 4022; https://doi.org/10.3390/math12244022 - 22 Dec 2024
Viewed by 628
Abstract
This study examines the spinor representations of TN (tangent and normal), NB (normal and binormal), TB (tangent and binormal) and TNB (tangent, normal and binormal)–Smarandache curves in three-dimensional Euclidean space E3. Spinors are complex column vectors and move on Pauli spin [...] Read more.
This study examines the spinor representations of TN (tangent and normal), NB (normal and binormal), TB (tangent and binormal) and TNB (tangent, normal and binormal)–Smarandache curves in three-dimensional Euclidean space E3. Spinors are complex column vectors and move on Pauli spin matrices. Isotropic vectors in the C3 complex vector space form a two-dimensional surface in the C2 complex space. Additionally, each isotropic vector in C3 space corresponds to two vectors in C2 space, called spinors. Based on this information, our goal is to establish a relationship between curve theory in differential geometry and spinor space by matching a spinor with an isotropic vector and a real vector generated from the vectors of the Frenet–Serret frame of a curve in three-dimensional Euclidean space. Accordingly, we initially assume two spinors corresponding to the Frenet–Serret frames of the main curve and its (TN, NB, TB and TNB)–Smarandache curves. Then, we utilize the relationships between the Frenet frames of these curves to examine the connections between the two spinors corresponding to these curves. Thus, we give the relationships between spinors corresponding to these Smarandache curves. For this reason, this study creates a bridge between mathematics and physics. This study can also serve as a reference for new studies in geometry and physics as a geometric interpretation of a physical expression. Full article
(This article belongs to the Special Issue Differential Geometric Structures and Their Applications)
18 pages, 343 KiB  
Article
The Lichnerowicz-Type Laplacians: Vanishing Theorems for Their Kernels and Estimate Theorems for Their Smallest Eigenvalues
by Josef Mikeš, Sergey Stepanov and Irina Tsyganok
Mathematics 2024, 12(24), 3936; https://doi.org/10.3390/math12243936 - 14 Dec 2024
Viewed by 559
Abstract
In the present paper, we prove several vanishing theorems for the kernel of the Lichnerowicz-type Laplacian and provide estimates for its lowest eigenvalue on closed Riemannian manifolds. As an example of the Lichnerowicz-type Laplacian, we consider the Hodge–de Rham Laplacian acting on forms [...] Read more.
In the present paper, we prove several vanishing theorems for the kernel of the Lichnerowicz-type Laplacian and provide estimates for its lowest eigenvalue on closed Riemannian manifolds. As an example of the Lichnerowicz-type Laplacian, we consider the Hodge–de Rham Laplacian acting on forms and ordinary Lichnerowicz Laplacian acting on symmetric tensors. Additionally, we prove vanishing theorems for the null spaces of these Laplacians and find estimates for their lowest eigenvalues on closed Riemannian manifolds with suitably bounded curvature operators of the first kind, sectional and Ricci curvatures. Specifically, we will prove our version of the famous differential sphere theorem, which we will apply to the aforementioned problems concerning the ordinary Lichnerowicz Laplacian. Full article
(This article belongs to the Special Issue Differential Geometric Structures and Their Applications)
9 pages, 264 KiB  
Article
Weak Quasi-Contact Metric Manifolds and New Characteristics of K-Contact and Sasakian Manifolds
by Vladimir Rovenski
Mathematics 2024, 12(20), 3230; https://doi.org/10.3390/math12203230 - 15 Oct 2024
Viewed by 1058
Abstract
Quasi-contact metric manifolds (introduced by Y. Tashiro and then studied by several authors) are a natural extension of contact metric manifolds. Weak almost-contact metric manifolds, i.e., where the linear complex structure on the contact distribution is replaced by a nonsingular skew-symmetric tensor, have [...] Read more.
Quasi-contact metric manifolds (introduced by Y. Tashiro and then studied by several authors) are a natural extension of contact metric manifolds. Weak almost-contact metric manifolds, i.e., where the linear complex structure on the contact distribution is replaced by a nonsingular skew-symmetric tensor, have been defined by the author and R. Wolak. In this paper, we study a weak analogue of quasi-contact metric manifolds. Our main results generalize some well-known theorems and provide new criterions for K-contact and Sasakian manifolds in terms of conditions on the curvature tensor and other geometric objects associated with the weak quasi-contact metric structure. Full article
(This article belongs to the Special Issue Differential Geometric Structures and Their Applications)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-4
Back to TopTop