Quadratic representation of a submanifold in pseudo-Euclidean space
type: Item
instance of: scholarly article
zbMATH Open document ID: 0989.53037
author: Chongzhen Ouyang
author: Tianzhen Qiu
publication date: 2001-09-04T00:00:00Z
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 1641150
zbMATH Keywords: isometric immersion
zbMATH Keywords: pseudo-Riemannian manifold
zbMATH Keywords: quadric representation
zbMATH Keywords: Laplacian operator
MaRDI profile type: Publication
title: Quadratic representation of a submanifold in pseudo-Euclidean space
review text: Let \(x\) be an isometric immersion of a pseudo-Riemannian manifold \(M\) in a pseudo-Euclidean space \(E\). The map \(\widetilde x=xx^t\) \((t\) denotes transpose) is called the quadric representation of \(M\). The authors study the map \(\widetilde x\) subject to one of the following conditions: (a) \(\widetilde x\) is of finite type; (b) \(\Delta\widetilde x=B\widetilde x+C\), where \(\Delta\) is the Laplacian operator and \(B\) and \(C\) are two constant matrices.NEWLINENEWLINEFor the entire collection see [Zbl 0954.00038].
reviewed by: Aurel Bejancu
description: scientific article; zbMATH DE number 1641150