Classification of minimal Lorentzian surfaces in $\mathbb S^4_2(1)$ with constant Gaussian and normal curvatures

Autor:	Dursun, Uğur, Turgay, Nurettin Cenk
Rok vydání:	2015
Předmět:	Mathematics - Differential Geometry 53B25 (Primary) 53C50 (Secondary)
Druh dokumentu:	Working Paper
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. Comment: Keywords. Gaussian curvature, minimal submanifolds, Lorentzian surfaces, normal curvature
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1508.03824 Zobrazit plný text záznamu View this record from Arxiv