Rigidity theorem for complete spacelike submanifold in \(S^{n+p}_q(1)\) with constant scalar curvature
type: Item
instance of: scholarly article
title: Rigidity theorem for complete spacelike submanifold in \(S^{n+p}_q(1)\) with constant scalar curvature
zbMATH Open document ID: 1262.53052
author: Shicheng Zhang
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2013-01-17T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1353695912
review text: The main theorem is as follows: Let \(M\) be a complete space-like \(n\)-submanifold of a Lorentzian space form of curvature 1. Assume that \(M\) has parallel mean curvature and constant scalar curvature \(\leq 1\). Assume furthermore that the squared norm of the second fundamental form of \(M\) is bounded from above by \(2\sqrt{n-1}\). Then \(M\) is either totally umbilical or isometric to a hyperbolic cylinder. The proof uses Cheng-Yau's technique from [\textit{S.-Y. Cheng} and \textit{S.-T. Yau}, Ann. Math. (2) 104, 407--419 (1976; Zbl 0352.53021)].
reviewed by: Ivan Izmestiev
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 6126487
zbMATH Keywords: semi-Riemannian manifold
zbMATH Keywords: space-like submanifolds
zbMATH Keywords: parallel mean curvature
zbMATH Keywords: constant scalar curvature
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6126487