Classification of minimal Lorentzian surfaces in $\mathbb S^4_2(1)$ with constant Gaussian and normal curvatures
| Autor: | Dursun, U��ur, Turgay, Nurettin Cenk |
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| Rok vydání: | 2015 |
| Předmět: | |
| DOI: | 10.48550/arxiv.1508.03824 |
| Popis: | In this paper we consider Lorentzian surfaces in the 4-dimensional pseudo-Riemannian sphere $\mathbb S^4_2(1)$ with index 2 of 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. Keywords. Gaussian curvature, minimal submanifolds, Lorentzian surfaces, normal curvature |
| Databáze: | OpenAIRE |
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