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Symmetry
Special Issues
Modern Geometry and Symmetries
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Modern Geometry and Symmetries

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (25 August 2022) | Viewed by 3585

Special Issue Editors

Prof. Dr. Branko Dragovich

E-Mail Website
Guest Editor
1. Institute of Physics, University of Belgrade, Belgrade, Serbia
2. Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia
Interests: modified gravity; cosmology; p-adic analysis; p-adic mathematical physics; p-adic string theory; genetic code and bioinformation
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Zoran Rakić

E-Mail Website
Guest Editor
Faculty of Mathematics, University of Belgrade, Belgrade, Serbia
Interests: geometry; mathematical physics

Special Issue Information

Dear Colleagues,

Modern Geometry is a rapidly developing branch of mathematics with plenty of applications, especially in sciences, engineering and arts. Symmetries under coordinate transformation and other transformations play a central role in geometry.
The goal of this Special Issue is to present a collection of recent advances in geometry, its symmetries and applications. Geometrical Seminar is a series of international scientific meetings on advances in geometry and its applications with a long tradition. The XXI Geometrical Seminar is postponed to be held face to face on June 26–July 2, 2022 in Belgrade, Serbia, http://poincare.matf.bg.ac.rs/~geometricalseminar/. We plan for selected papers of contributions to the XXI Geometrical Seminar to make up a significant part of this Special Issue. Other submissions are also very welcome.

Prof. Dr. Branko Dragovich
Prof. Dr. Zoran Rakić
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. Symmetry 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

  • differential geometry
  • topology
  • Lie groups
  • mathematical physics
  • discrete geometry
  • integrable systems
  • visualization

Published Papers (2 papers)

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Research

21 pages, 1289 KiB  
Article
Recurrent Generalization of F-Polynomials for Virtual Knots and Links
by Amrendra Gill, Maxim Ivanov, Madeti Prabhakar and Andrei Vesnin
Symmetry 2022, 14(1), 15; https://doi.org/10.3390/sym14010015 - 23 Dec 2021
Cited by 1 | Viewed by 1872
Abstract
F-polynomials for virtual knots were defined by Kaur, Prabhakar and Vesnin in 2018 using flat virtual knot invariants. These polynomials naturally generalize Kauffman’s affine index polynomial and use smoothing in the classical crossing of a virtual knot diagram. In this paper, we introduce [...] Read more.
F-polynomials for virtual knots were defined by Kaur, Prabhakar and Vesnin in 2018 using flat virtual knot invariants. These polynomials naturally generalize Kauffman’s affine index polynomial and use smoothing in the classical crossing of a virtual knot diagram. In this paper, we introduce weight functions for ordered orientable virtual and flat virtual links. A flat virtual link is an equivalence class of virtual links with respect to a local symmetry changing a type of classical crossing in a diagram. By considering three types of smoothing in classical crossings of a virtual link diagram and suitable weight functions, there is provided a recurrent construction for new invariants. It is demonstrated by explicit examples that newly defined polynomial invariants are stronger than F-polynomials. Full article
(This article belongs to the Special Issue Modern Geometry and Symmetries)
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11 pages, 281 KiB  
Article
An Infinite Family of Compact, Complete, and Locally Affine k-Symplectic Manifolds of Dimension Three
by Fanich El Mokhtar and Essabab Said
Symmetry 2021, 13(11), 2159; https://doi.org/10.3390/sym13112159 - 11 Nov 2021
Viewed by 976
Abstract
We study the complete, compact, locally affine manifolds equipped with a k-symplectic structure, which are the quotients of Rn(k+1) by a subgroup Γ of the affine group A(n(k+1)) [...] Read more.
We study the complete, compact, locally affine manifolds equipped with a k-symplectic structure, which are the quotients of Rn(k+1) by a subgroup Γ of the affine group A(n(k+1)) of Rn(k+1) acting freely and properly discontinuously on Rn(k+1) and leaving invariant the k-symplectic structure, then we construct and give some examples and properties of compact, complete, locally affine two-symplectic manifolds of dimension three. Full article
(This article belongs to the Special Issue Modern Geometry and Symmetries)
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