Singular Minimal Surfaces which are Minimal

Muhittin Evren Aydın; Ayla Erdur Kara; Mahmut Ergüt

doi:10.32323/ujma.984462

EN

Singular Minimal Surfaces which are Minimal

Abstract

In the present paper, we discuss the singular minimal surfaces in Euclidean $3-$space $\mathbb{R}^{3}$ which are minimal. 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 $\mathbb{R}^{3}$. 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.

Keywords

Minimal surface, Semi-symmetric connection, Singular minimal surface, Translation surface

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Muhittin Evren Aydın
0000-0001-9337-8165
Türkiye

Ayla Erdur Kara ^*
Türkiye

Mahmut Ergüt
0000-0002-9098-8280
Türkiye

Publication Date

December 30, 2021

Submission Date

August 18, 2021

Acceptance Date

December 23, 2021

Published in Issue

Year 2021 Volume: 4 Number: 4

DOI

https://doi.org/10.32323/ujma.984462

IZ

https://izlik.org/JA99JC42PD

APA

Aydın, M. E., Erdur Kara, A., & Ergüt, M. (2021). Singular Minimal Surfaces which are Minimal. Universal Journal of Mathematics and Applications, 4(4), 136-146. https://doi.org/10.32323/ujma.984462

AMA

1.Aydın ME, Erdur Kara A, Ergüt M. Singular Minimal Surfaces which are Minimal. Univ. J. Math. Appl. 2021;4(4):136-146. doi:10.32323/ujma.984462

Chicago

Aydın, Muhittin Evren, Ayla Erdur Kara, and Mahmut Ergüt. 2021. “Singular Minimal Surfaces Which Are Minimal”. Universal Journal of Mathematics and Applications 4 (4): 136-46. https://doi.org/10.32323/ujma.984462.

EndNote

Aydın ME, Erdur Kara A, Ergüt M (December 1, 2021) Singular Minimal Surfaces which are Minimal. Universal Journal of Mathematics and Applications 4 4 136–146.

IEEE

[1]M. E. Aydın, A. Erdur Kara, and M. Ergüt, “Singular Minimal Surfaces which are Minimal”, Univ. J. Math. Appl., vol. 4, no. 4, pp. 136–146, Dec. 2021, doi: 10.32323/ujma.984462.

ISNAD

Aydın, Muhittin Evren - Erdur Kara, Ayla - Ergüt, Mahmut. “Singular Minimal Surfaces Which Are Minimal”. Universal Journal of Mathematics and Applications 4/4 (December 1, 2021): 136-146. https://doi.org/10.32323/ujma.984462.

JAMA

1.Aydın ME, Erdur Kara A, Ergüt M. Singular Minimal Surfaces which are Minimal. Univ. J. Math. Appl. 2021;4:136–146.

MLA

Aydın, Muhittin Evren, et al. “Singular Minimal Surfaces Which Are Minimal”. Universal Journal of Mathematics and Applications, vol. 4, no. 4, Dec. 2021, pp. 136-4, doi:10.32323/ujma.984462.

Vancouver

1.Muhittin Evren Aydın, Ayla Erdur Kara, Mahmut Ergüt. Singular Minimal Surfaces which are Minimal. Univ. J. Math. Appl. 2021 Dec. 1;4(4):136-4. doi:10.32323/ujma.984462