Space-like hypersurfaces with constant scalar curvature in the de Sitter spaces
type: Item
instance of: scholarly article
title: Space-like hypersurfaces with constant scalar curvature in the de Sitter spaces
zbMATH Open document ID: 0848.53035
DOI: 10.1016/0926-2245(96)00006-X
author: Yongfan Zheng
published in: Differential Geometry and its Applications
publication date: 1996-07-07T00:00:00Z
review text: The author proves the following Theorem: Let \(M^n\) be an \(n\)-dimensional compact space-like hypersurface in \(M^{n+1}_1 (c)\) with constant scalar curvature. If \(M^n\) satisfies \(K(M) > 0\), \(\text{Ric} (M) \leq (n -1)c\), \(R \leq c\), where \(R\) is the normalized scalar curvature of \(M^n\), then \(M^n\) is totally umbilical.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 897465
zbMATH Keywords: de Sitter spaces
zbMATH Keywords: sectional curvature
zbMATH Keywords: compact space-like hypersurface
zbMATH Keywords: scalar curvature
zbMATH Keywords: totally umbilical
Wikidata QID: Q115362521
reviewed by: Bernard Rouxel
MaRDI profile type: Publication
cites work: On spacelike hypersurfaces with constant mean curvature in the de Sitter space
cites work: Complete space-like submanifolds in a de Sitter space with parallel mean curvature vector
cites work: Hypersurfaces with constant scalar curvature
cites work: Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces
cites work: Q3312869
cites work: Q3029747
cites work: Submanifolds with Constant Mean Curvature II
full work available at URL: 0926-2245(96)00006-x
OpenAlex ID: W1999246980
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description: scientific article; zbMATH DE number 897465