On nonimmersibility of compact hypersurfaces into a ball of a simply connected space form
type: Item
instance of: scholarly article
title: On nonimmersibility of compact hypersurfaces into a ball of a simply connected space form
zbMATH Open document ID: 0864.53039
DOI: 10.1007/BF02762695
author: Fernando Giménez
author: Vicente Miquel
published in: Israel Journal of Mathematics
publication date: 1996-07-14T00:00:00Z
review text: Let \(M\) be a compact hypersurface of some standard space \(\mathbb{K}^n (\lambda)\) of constant curvature \(\lambda\) lying in a ball \(B_R\subset \mathbb{K}^n(\lambda)\) of some radius \(R\). The authors give a characterization for \(M=\partial B_R\) in terms of two inequalities in which integrals over the Ricci and scalar curvature of \(M\) are involved. As essential tool they derive an integral formula which for \(\lambda=0\) reduces to the Minkowski formula.
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 902612
zbMATH Keywords: hypersurfaces of spaces of constant curvature
zbMATH Keywords: integral formula of Minkowski type
reviewed by: Helmut Reckziegel
MaRDI profile type: Publication
Wikidata QID: Q125581946
cites work: Isometric embedding of a compact Riemannian manifold into sphere
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full work available at URL: https://doi.org/10.1007/bf02762695
OpenAlex ID: W2078758743
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description: scientific article; zbMATH DE number 902612