Differentiable rigidity of hypersurface in space forms
type: Item
instance of: scholarly article
title: Differentiable rigidity of hypersurface in space forms
zbMATH Open document ID: 1320.53049
author: Pak Tung Ho
published in: Manuscripta Mathematica
publication date: 2015-03-23T00:00:00Z
review text: In the main theorem of the paper under review the author proves a rigidity theorem for three-dimensional compact hypersurfaces \(M\) in a four-dimensional space form. The assumptions are the positivity of the scalar curvature and an integral inequality for the squared length of the second fundamental form. A similar result is shown for four-dimensional hypersurfaces in a five-dimensional space form where the inequality involves also the norm of the Weyl tensor. The rigidity is only topological in these cases, i.e., \(M\) is shown to be diffeomorphic with a standard space.
Mathematics Subject Classification ID: 53C24
Mathematics Subject Classification ID: 58C40
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 6418376
zbMATH Keywords: scalar curvature
zbMATH Keywords: second fundamental form
zbMATH Keywords: Weyl tensor
zbMATH Keywords: Yamabe invariant
reviewed by: Wolfgang Kühnel
MaRDI profile type: Publication
full work available at URL: s00229-014-0709-3
OpenAlex ID: W2024305824
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Wikidata QID: Q126122685
DOI: 10.1007/S00229-014-0709-3
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description: scientific article; zbMATH DE number 6418376