Special Issue "Differential Geometry of Special Mappings"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 30 April 2019

Special Issue Editor

Guest Editor
Prof. Dr. Josef Mikeš

Department of Algebra and Geometry, Palacky University, 17. listopadu 12, 771 46 Olomouc, Czech Republic
Website | E-Mail
Interests: differential geometry of (pseudo-) Riemannian manifolds and manifolds with connections; theory of geodesic, conformal, holomorphically-projective mappings of special manifolds

Special Issue Information

Dear Colleagues,

It is very well known that differential geometry studies a number of interesting problems, and the geometry has very applicable potential. There are many applications to (pseudo-) Riemannian and Finsler geometry, and also to the geometry of manifolds with affine and projective connections (e.g., special mappings of manifolds–geodesic, conformal, holomorphically-projective mappings, transformations and deformations), variational theory and physics.

The purpose of this Special Issue is to bring mathematicians together with physicists, as well as other scientists, for whom differential geometry is a valuable research tool.

This Special Issue deals with the theory and applications of differential geometry, especially in physics, and will accept high-quality papers having original research results. The Guest Editor solicits papers dealing with these challenging questions in the language of mathematics.

Prof. Dr. Josef Mikeš
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 papers will be 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 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 850 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

  • Differentiable manifolds
  • Geometry of spaces with structures
  • (pseudo-) Riemannian geometry
  • Geodesics and their generalizations
  • Special mappings and transformations
  • Differential invariants
  • Variational theory on manifolds
  • Applications to physics

Published Papers (2 papers)

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Research

Open AccessArticle Classification of Warped Product Submanifolds in Kenmotsu Space Forms Admitting Gradient Ricci Solitons
Mathematics 2019, 7(2), 112; https://doi.org/10.3390/math7020112
Received: 2 January 2019 / Revised: 14 January 2019 / Accepted: 18 January 2019 / Published: 22 January 2019
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Abstract
The purpose of this article is to obtain geometric conditions in terms of gradient Ricci curvature, both necessary and sufficient, for a warped product semi-slant in a Kenmotsu space form, to be either CR-warped product or simply a Riemannian product manifold when a [...] Read more.
The purpose of this article is to obtain geometric conditions in terms of gradient Ricci curvature, both necessary and sufficient, for a warped product semi-slant in a Kenmotsu space form, to be either CR-warped product or simply a Riemannian product manifold when a basic inequality become equality. The next purpose of this paper to find the necessary condition admitting gradient Ricci soliton, that the warped product semi-slant submanifold of Kenmotsu space form, is an Einstein warped product. We also discuss some obstructions to these constructions in more detail. Full article
(This article belongs to the Special Issue Differential Geometry of Special Mappings)
Open AccessArticle Higher Order Hamiltonian Systems with Generalized Legendre Transformation
Mathematics 2018, 6(9), 163; https://doi.org/10.3390/math6090163
Received: 9 August 2018 / Revised: 27 August 2018 / Accepted: 4 September 2018 / Published: 10 September 2018
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Abstract
The aim of this paper is to report some recent results regarding second order Lagrangians corresponding to 2nd and 3rd order Euler–Lagrange forms. The associated 3rd order Hamiltonian systems are found. The generalized Legendre transformation and geometrical correspondence between solutions of the Hamilton [...] Read more.
The aim of this paper is to report some recent results regarding second order Lagrangians corresponding to 2nd and 3rd order Euler–Lagrange forms. The associated 3rd order Hamiltonian systems are found. The generalized Legendre transformation and geometrical correspondence between solutions of the Hamilton equations and the Euler–Lagrange equations are studied. The theory is illustrated on examples of Hamiltonian systems satisfying the following conditions: (a) the Hamiltonian system is strongly regular and the Legendre transformation exists; (b) the Hamiltonian system is strongly regular and the Legendre transformation does not exist; (c) the Legendre transformation exists and the Hamiltonian system is not regular but satisfies a weaker condition. Full article
(This article belongs to the Special Issue Differential Geometry of Special Mappings)
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