Complete maximal spacelike hypersurfaces of \(H_ 1^ 4(c)\)
type: Item
instance of: scholarly article
title: Complete maximal spacelike hypersurfaces of \(H_ 1^ 4(c)\)
zbMATH Open document ID: 0804.53088
DOI: 10.1007/BF02567694
author: Qing-Ming Cheng
published in: Manuscripta Mathematica
publication date: 1995-01-22T00:00:00Z
full work available at URL: https://eudml.org/doc/155924
review text: The author proves the following theorems: Theorem 1. Let \(M\) be a maximal complete 3-dimensional spacelike hypersurface of \(H^ 4_ 1(c)\) [4-dimensional anti-de Sitter space of constant curvature] with non-zero constant Gauss-Kronecker curvature. Then \(M\) is the hyperbolic cylinder \(H^ 1(c_ 1)\times H^ 2(c_ 2)\). Theorem 2. Let \(M\) be a 3-dimensional complete maximal spacelike hypersurface of \(H^ 4_ 1(c)\) with constant scalar curvature and \(\inf k^ 2>0\), where \(k\) is the Gauss-Kronecker curvature. Then \(M\) is the cylinder \(H^ 1(c_ 1)\times H^ 2(c_ 2)\). Theorem 3. There are no complete maximal spacelike hypersurfaces in \(H^ 4_ 1(c)\) with constant scalar and \(\sup k^ 2<{S^ 3\over S^ 4}\), where \(k\) is the Gauss-Kronecker curvature and \(S\) is the squared norm of the second fundamental form.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 599655
zbMATH Keywords: anti-de Sitter space
zbMATH Keywords: constant Gauss-Kronecker curvature
zbMATH Keywords: hyperbolic cylinder
zbMATH Keywords: constant scalar curvature
reviewed by: Bernard Rouxel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 599655