Reduction of codimension of surfaces
type: Item
instance of: scholarly article
title: Reduction of codimension of surfaces
zbMATH Open document ID: 0686.53049
DOI: 10.1007/BF00147478
author: J.-H. Eschenburg
author: Renato de Azevedo Tribuzy
published in: Geometriae Dedicata
publication date: 1989-01-01T00:00:00Z
review text: Let x: \(M^ 2\to Q^ n\) be a smooth immersion of a two-manifold \(M^ 2\) into a space form Q such that its mean curvature vector lies in a parallel subbundle E of its normal bundle. The authors show that the codimension of x can be reduced to the following values k under suitable assumptions: 1) If x is analytic then \(k=\dim E+1\) or \(x(M^ 2)\) is minimal in an (n-dim E)-dimensional totally umbilic submanifold of \(Q^ n\). 2) If \(M^ 2\) is a 2-sphere then \(k=\dim E\) or \(x(M^ 2)\) is minimal as above. [Due to some undefined notation in the main theorems this has to be concluded from the proofs given in this paper.]
reviewed by: Bernd Wegner
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 4124540
zbMATH Keywords: two-manifold
zbMATH Keywords: mean curvature vector
zbMATH Keywords: parallel subbundle
zbMATH Keywords: codimension
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00147478
OpenAlex ID: W2059668966
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description: scientific article; zbMATH DE number 4124540