Compact spacelike surfaces in the 3-dimensional de Sitter space with non-degenerate second fundamental form.
type: Item
instance of: scholarly article
title: Compact spacelike surfaces in the 3-dimensional de Sitter space with non-degenerate second fundamental form.
zbMATH Open document ID: 1041.53037
DOI: 10.1016/S0926-2245(03)00019-6
author: Juan A. Aledo
author: Alfonso Romero
published in: Differential Geometry and its Applications
publication date: 2003-08-25T00:00:00Z
review text: The authors study the geometry of a compact spacelike surface \(M\) in the de Sitter space \(S^3_1\). It is known that the totally umbilical round spheres are the only compact spacelike surfaces with constant Gaussian curvatute \(K < 1\). Using this result, they prove the following: For a compact spacelike surface \(M\) in \(S^3_1\) with Gaussian curvature \(K < 1\), the following assersions are equivalent: (i) \(K\) is constant (ii) The Gaussian curvature of the second fundamental form is constant. (iii) \(M\) is a totally umbilical round sphere.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53B30
zbMATH DE Number: 1970813
zbMATH Keywords: de Sitter space
zbMATH Keywords: compact spacelike surface
zbMATH Keywords: second fundamental form
zbMATH Keywords: Gaussian curvature
zbMATH Keywords: totally umbilical
Wikidata QID: Q115338041
reviewed by: Krishan Lal Duggal
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1970813