Rigidity of real Kaehler submanifolds
type: Item
instance of: scholarly article
title: Rigidity of real Kaehler submanifolds
zbMATH Open document ID: 0599.53005
DOI: 10.1215/S0012-7094-86-05314-7
author: Marcos Dajczer
author: Lucio L. Rodriguez
published in: Duke Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: This paper deals with isometric immersions f of 2n-dimensional Kaehler manifolds into real Euclidean \((2n+p)\)-space. If the type number is at least 3, then f is holomorphic. If f is minimal, then it is circular (i.e. \(\alpha (JX,Y)=\alpha (X,JY))\), and thus the results of the first author and \textit{D. Gromoll} [J. Differ. Geom. 22, 13-28 (1985; Zbl 0587.53051)] apply. If f is minimal, then it is congruent to a holomorphic isometric immersion into \({\mathbb{C}}^{n+1}\), if such exist. For type number 3 a similar result holds in \({\mathbb{C}}^{n+q}\). The core of the proofs is a lemma on the determination of the second fundamental form by the Gauss equation generalizing a well-known result of Chern.
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53B35
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 3967325
zbMATH Keywords: real holomorphic immersions
zbMATH Keywords: circular immersions
zbMATH Keywords: flat bilinear forms
zbMATH Keywords: Gauss equation
reviewed by: Dirk Ferus
MaRDI profile type: Publication
Wikidata QID: Q125917913
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full work available at URL: s0012-7094-86-05314-7
OpenAlex ID: W2068390497
description: scientific article; zbMATH DE number 3967325