Immersed hypersurfaces in the unit sphere \(S^{m+1}\) with constant Blaschke eigenvalues
type: Item
instance of: scholarly article
title: Immersed hypersurfaces in the unit sphere \(S^{m+1}\) with constant Blaschke eigenvalues
zbMATH Open document ID: 1151.53013
author: Feng Yun Zhang
author: Xingxiao Li
publication date: 2007-06-07T00:00:00Z
review text: Let \(x:M^m \rightarrow S^{m+p}\) be an immersion into the sphere \(S^{m+p}\) without umbilic points. One can introduce the following Möbius invariants: The Möbius metric \(g,\) the Möbius form \(\phi,\) the Blaschke tensor \(A,\) and the Möbius second fundamental form \(B.\) The eigenvalues of \(B\) are called \textit{Möbius principal curvatures,} the eigenvalues of \(A\) are called \textit{Blaschke eigenvalues.} In this paper a classification of hypersurfaces \(x:M^{m}\rightarrow S^{m+1}\) with vanishing Möbius form and two constant and distinct Blaschke eigenvalues is presented. Another result is the classification of immersed and umbilic free hypersurfaces in \(S^4\) with vanishing Möbius form and constant Blaschke eigenvalues.
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 53B25
zbMATH DE Number: 5162331
zbMATH Keywords: Möbius form
zbMATH Keywords: Blaschke tensor
zbMATH Keywords: Blaschke eigenvalues, Möbius metric, Möbius second fundamental form
reviewed by: Hans-Bert Rademacher
MaRDI profile type: Publication
full work available at URL: s10114-005-0919-4
OpenAlex ID: W2057848507
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DOI: 10.1007/S10114-005-0919-4
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5162331