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2016 Classification of Minimal Lorentzian Surfaces in $\mathbb{S}^4_2(1)$ with Constant Gaussian and Normal Curvatures
Uğur Dursun, Nurettin Cenk Turgay
Taiwanese J. Math. 20(6): 1295-1311 (2016). DOI: 10.11650/tjm.20.2016.7345

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.

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Uğur Dursun. Nurettin Cenk Turgay. "Classification of Minimal Lorentzian Surfaces in $\mathbb{S}^4_2(1)$ with Constant Gaussian and Normal Curvatures." Taiwanese J. Math. 20 (6) 1295 - 1311, 2016. https://doi.org/10.11650/tjm.20.2016.7345

Information

Published: 2016
First available in Project Euclid: 1 July 2017

zbMATH: 1357.53026
MathSciNet: MR3580296
Digital Object Identifier: 10.11650/tjm.20.2016.7345

Subjects:
Primary: 53B25
Secondary: 53C50

Rights: Copyright © 2016 The Mathematical Society of the Republic of China

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Vol.20 • No. 6 • 2016
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