Space-like submanifolds with constant scalar curvature
type: Item
instance of: scholarly article
title: Space-like submanifolds with constant scalar curvature
zbMATH Open document ID: 986.53021
author: Ximin Liu
published in: Comptes Rendus de l'Académie des Sciences. Série I. Mathématique
publication date: 0001-01-01T00:00:00Z
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 1643171
zbMATH Keywords: de Sitter space
zbMATH Keywords: space-like submanifold
zbMATH Keywords: sectional curvature
zbMATH Keywords: scalar curvature
zbMATH Keywords: totally umbilic
MaRDI profile type: Publication
DOI: 10.1016/S0764-4442(01)01921-8
review text: The main result of this paper is the following: Let \(M^n\) be an \(n\)-dimensional compact space-like submanifold with constant scalar curvature and nonnegative sectional curvature immersed in a de Sitter space \(M_p^{n+p}(c).\) If \(M^n\) has flat normal bundle and the normalized scalar curvature \(R\) of \(M^n\) satisfies \(R<c,\) then \(M^n\) is totally umbilical and isometric to a sphere.
reviewed by: Christos Baikoussis
description: scientific article; zbMATH DE number 1643171