Singular Minimal Surfaces which are Minimal

Autor:	Muhittin Evren AYDIN, Ayla ERDUR KARA, Mahmut ERGÜT
Rok vydání:	2021
Předmět:	Mathematics - Differential Geometry Minimal surface Semi-symmetric connection Singular minimal surface Translation surface Matematik Differential Geometry (math.DG) FOS: Mathematics General Medicine Mathematics
Zdroj:	Volume: 4, Issue: 4 136-146 Universal Journal of Mathematics and Applications
ISSN:	2619-9653
DOI:	10.32323/ujma.984462
Popis:	In the present paper, we discuss the singular minimal surfaces in a Euclidean 3-space R^{3} which are minimal. In fact, such a surface is nothing but a plane, a trivial outcome. However, a non-trivial outcome is obtained when we modify the usual condition of singular minimality by using a special semi-symmetric metric connection instead of the Levi-Civita connection on R^{3}. With this new connection, we prove that, besides planes, the singular minimal surfaces which are minimal are the generalized cylinders, providing their explicit equations. A trivial outcome is observed when we use a special semi-symmetric non-metric connection. Furthermore, our discussion is adapted to the Lorentz-Minkowski 3-space. 15 pages
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2f3cf7ab70ee0934350f60c5a672c567 https://doi.org/10.32323/ujma.984462 Zobrazit plný text záznamu