Taiwanese Journal of Mathematics

Classification of Minimal Lorentzian Surfaces in $\mathbb{S}^4_2(1)$ with Constant Gaussian and Normal Curvatures

Uğur Dursun and Nurettin Cenk Turgay

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Abstract

In this paper we consider Lorentzian surfaces in the $4$-dimensional pseudo-Riemannian sphere $\mathbb{S}^4_2(1)$ with index $2$ and curvature one. We obtain the complete classification of minimal Lorentzian surfaces $\mathbb{S}^4_2(1)$ whose Gaussian and normal curvatures are constants. We conclude that such surfaces have the Gaussian curvature $1/3$ and the absolute value of normal curvature $2/3$. We also give some explicit examples.

Article information

Source
Taiwanese J. Math., Volume 20, Number 6 (2016), 1295-1311.

Dates
First available in Project Euclid: 1 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1498874532

Digital Object Identifier
doi:10.11650/tjm.20.2016.7345

Mathematical Reviews number (MathSciNet)
MR3580296

Zentralblatt MATH identifier
1357.53026

Subjects
Primary: 53B25: Local submanifolds [See also 53C40]
Secondary: 53C50: Lorentz manifolds, manifolds with indefinite metrics

Keywords
Gaussian curvature minimal submanifolds Lorentzian surfaces normal curvature

Citation

Dursun, Uğur; Turgay, Nurettin Cenk. Classification of Minimal Lorentzian Surfaces in $\mathbb{S}^4_2(1)$ with Constant Gaussian and Normal Curvatures. Taiwanese J. Math. 20 (2016), no. 6, 1295--1311. doi:10.11650/tjm.20.2016.7345. https://projecteuclid.org/euclid.twjm/1498874532


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