On the Gauss equation of an isometric immersion
type: Item
instance of: scholarly article
title: On the Gauss equation of an isometric immersion
zbMATH Open document ID: 0545.53016
DOI: 10.1215/S0012-7094-84-05121-4
author: Siegfried Steiner
author: Jaak Vilms
author: Eberhard Teufel
published in: Duke Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: The authors investigate the algebraic problem to represent a curvature like tensor R (on an n-dimensional linear space) by the right side of Gauß equation (of submanifolds in Euclidean space) involving the least possible number cl(R) of symmetric bilinear forms. They give a constructive proof for \(cl(R)\leq\binom{n}{2}\). In fact, \(cl(R)\leq\binom{n}{2}-(n-3)\) [cf. \textit{E. Berger, R. Bryant} and \textit{P. Griffiths}, Duke Math. J. 50, 803-892 (1983; Zbl 0526.53018)]. The authors prove the usefulness of their method by using it to derive again several well-known facts, for instance the Allendoerfer-Chern ''type number and rigidity'' theorem.
Mathematics Subject Classification ID: 53B21
Mathematics Subject Classification ID: 53B25
zbMATH DE Number: 3868143
zbMATH Keywords: embedding problem
zbMATH Keywords: curvature like tensor
zbMATH Keywords: Gauß equation
reviewed by: Helmut Reckziegel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3868143