On complete space-like submanifolds with parallel mean curvature vector
type: Item
instance of: scholarly article
title: On complete space-like submanifolds with parallel mean curvature vector
zbMATH Open document ID: 0918.53019
author: Yuxing Dong
author: Yi-Bing Shen
published in: Chinese Annals of Mathematics. Series B
publication date: 1999-08-10T00:00:00Z
review text: It is proved that in a complete spacelike submanifold \(M^{n}\) with parallel mean curvature vector field of an indefinite space form \(N_p^{n+p}(c)\), the second fundamental form of \(M^n\) is upper bounded. This result is generalized to spacelike hypersurfaces with constant mean curvature in a Lorentz manifold. Also, harmonic Gauss maps of \(M^n\) in \(N_p^{n+p}(c)\) are investigated.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 1199837
zbMATH Keywords: spacelike submanifold
zbMATH Keywords: parallel mean curvature vector
zbMATH Keywords: indefinite space form
zbMATH Keywords: second fundamental form
zbMATH Keywords: constant mean curvature
zbMATH Keywords: harmonic Gauss maps
reviewed by: Constantin Călin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1199837