Integral inequalities for maximal space-like submanifolds in the indefinite space form
type: Item
instance of: scholarly article
zbMATH Open document ID: 1002.53044
publication date: 2002-02-19T00:00:00Z
full work available at URL: https://eudml.org/doc/122285
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 1702484
zbMATH Keywords: maximal spacelike submanifold
zbMATH Keywords: indefinite space form
zbMATH Keywords: flat normal bundle
author: Ximin Liu
MaRDI profile type: Publication
title: Integral inequalities for maximal space-like submanifolds in the indefinite space form
published in: Balkan Journal of Geometry and its Applications (BJGA)
review text: Let \(M^n\) be an \(n\)-dimensional Riemannian manifold immersed in \(M_p^{n+p} (c)\), where \(M_p^{n+p}(c)\) is an \((n+p)\)-dimensional connected semi-Riemannian manifold of constant curvature \(c\). If the semi-Riemannian metric of \(M_p^{n+p} (c)\) induces the Riemannian metric on \(M^n\), \(M^n\) is called a space-like submanifold. Such a submanifold with vanishing mean curvature is called a maximal space-like submanifold. The author gives intrinsic integral inequalities for compact maximal space-like submanifolds and a sufficient and necessary condition for such a submanifold to be totally geodesic.
reviewed by: Friedrich Manhart
description: scientific article; zbMATH DE number 1702484