On space-like hypersurfaces in the de Sitter space
type: Item
instance of: scholarly article
title: On space-like hypersurfaces in the de Sitter space
zbMATH Open document ID: 0863.53040
DOI: 10.1007/BF00773403
author: Yongfan Zheng
published in: Annals of Global Analysis and Geometry
publication date: 1997-05-28T00:00:00Z
review text: The author investigates compact spacelike hypersurfaces in \(S^{n+1}_1\), where \(S^{n+1}_1\) is the (\(n+1\))-dimensional Lorentzian space form of positive constant curvature \(c\), often called de Sitter space. The author proves the following Theorem: Let \(M^n\) be an \(n\)-dimensional compact spacelike hypersurface in \(S^{n+1}_1\) with constant scalar curvature. If \(M^n\) satisfies \[ K(M)\geq 0,\quad R<c, \] where \(R\) is the normalized scalar curvature of \(M^n\), then \(M^n\) is isometric to a sphere. This improves a previous result of the author on such hypersurfaces.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 839168
zbMATH Keywords: de Sitter space
zbMATH Keywords: spacelike hypersurfaces
zbMATH Keywords: scalar curvature
reviewed by: M. Magid
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: COMPLETE SPACE-LIKE HYPERSURFACES OF A DE SITTER SPACE WITH r = kH
cites work: Hypersurfaces with constant scalar curvature
cites work: Q3029747
cites work: Space-like hypersurfaces with constant scalar curvature in the de Sitter spaces
full work available at URL: https://doi.org/10.1007/bf00773403
OpenAlex ID: W2312971335
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description: scientific article; zbMATH DE number 839168