Mixed foliate CR-submanifolds of indefinite complex space-forms
type: Item
instance of: scholarly article
title: Mixed foliate CR-submanifolds of indefinite complex space-forms
zbMATH Open document ID: 0652.53038
DOI: 10.1007/BF01773928
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1987-01-01T00:00:00Z
review text: Let M be a CR-submanifold of a Kähler manifold \(\tilde M\) and D and \(D^{\perp}\) be the distributions carried by M [see the reviewer, Geometry of CR-submanifolds (Reidel 1986; Zbl 0605.53001)]. Then M is called mixed foliate if D is integrable and the second fundamental form h of M satisfies \(h(X,Y)=0\), for any X and Y from D and \(D^{\perp}\) respectively. In the present paper a mixed foliate proper CR-submanifold M of an indefinite complex space-form \(\tilde M(c)\) is considered and it is proved that \(c=0\), provided the restrictions of the metric to D and \(D^{\perp}\) are definite and indefinite, respectively. More results are obtained with respect to CR-submanifolds which have flat normal connection and parallelizable totally real distribution.
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 4063986
zbMATH Keywords: distributions
zbMATH Keywords: mixed foliate proper CR-submanifold
zbMATH Keywords: indefinite complex space-form
zbMATH Keywords: flat normal connection
author: Ramesh Sharma
author: Krishan Lal Duggal
reviewed by: Aurel Bejancu
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01773928
OpenAlex ID: W2048859782
description: scientific article; zbMATH DE number 4063986