On the curvatures of complete spacelike hypersurfaces in de Sitter space
type: Item
instance of: scholarly article
title: On the curvatures of complete spacelike hypersurfaces in de Sitter space
zbMATH Open document ID: 0969.53034
DOI: 10.1023/A:1005204512349
author: Juan A. Aledo
author: Luis J. Alías
published in: Geometriae Dedicata
publication date: 2000-01-01T00:00:00Z
review text: Let \(M^n\) be a complete spacelike hypersurface in the de Sitter space \(S^{n+1}_1\subset L^{n+2}\), whose sectional curvature are bounded away from \(-\infty\). Let \(M^n\) be contained in the region \(\Omega(a,r)= \{x\in S^{n+1}_1:\langle a,x\rangle\leq -\sinh(r)< 0\}\) for a timelike direction \(a\in L^{n+2}\) and a positive real number \(r>0\). It is proved that then \(\sup H_j\geq \tanh(r)^j\) and \(\text{inf Ric}(v,v)\leq {n-1\over\cosh^2(r)}\), where \(H_j\) is the \(j\)th mean curvature, \(\text{Ric}(X,Y)\) is the Ricci curvature and \(v\) is a tangent to \(M^n\) vector with \(|v|= 1\). In the proofs a generalized maximum principle is used, due to \textit{H. Omori} [J. Math. Soc. Jap. 19, 205-214 (1967; Zbl 0154.21501)].
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 1485575
zbMATH Keywords: de Sitter space
zbMATH Keywords: spacelike hypersurface
zbMATH Keywords: higher-order mean curvature
zbMATH Keywords: Ricci curvature
zbMATH Keywords: generalized maximum principle
MaRDI profile type: Publication
full work available at URL: a:1005204512349
OpenAlex ID: W121432537
description: scientific article; zbMATH DE number 1485575