Rigidity of CR submanifolds and analyticity of CR immersions
type: Item
instance of: scholarly article
title: Rigidity of CR submanifolds and analyticity of CR immersions
zbMATH Open document ID: 0676.32004
DOI: 10.1007/BF01446890
author: Chong-Kyu Han
published in: Mathematische Annalen
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164682
review text: Let M and \(\tilde M\) be real analytic CR manifolds of hypersurface type of dimension \(2n+1\) and \(2\tilde n+1\), respectively, where \(n<\tilde n\). Let f be a CR immersion of M into \(\tilde M.\) Suppose that \(\tilde M\) is strongly pseudoconvex and f is of differentiability class \({\mathcal C}^ 5\) and f is rigid at every point of M. Then f is real analytic. In particular, a \({\mathcal C}^ 5\) immersion of a real analytic CR manifold of dimension 2n-1 into the sphere \(S^{2n+1}\) is real analytic if \(n\geq 4\).
Mathematics Subject Classification ID: 32V40
Mathematics Subject Classification ID: 32C05
Mathematics Subject Classification ID: 32T99
zbMATH DE Number: 4107184
zbMATH Keywords: real analytic CR manifolds
zbMATH Keywords: CR immersion
zbMATH Keywords: strongly pseudoconvex
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4107184