Totally umbilical CR-submanifolds of semi-Riemannian Kähler manifolds
type: Item
instance of: scholarly article
title: Totally umbilical CR-submanifolds of semi-Riemannian Kähler manifolds
zbMATH Open document ID: 0624.53030
DOI: 10.1155/S0161171287000668
author: Krishan Lal Duggal
author: Ramesh Sharma
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46203
review text: Let M be a totally umbilical CR-submanifold of a Kähler manifold \(\tilde M\) endowed with a semi-Riemannian metric and \(D^{\perp}\) be the totally real distribution [see the reviewer, Geometry of CR-submanifolds (1986; Zbl 0605.53001)]. The authors prove: (i) if dim \(D^{\perp}>1\), then M is a CR-product and (ii) if dim \(D^{\perp}=1\), then M has a normal contact metric structure if and only if it has parallel second fundamental form.
reviewed by: Aurel Bejancu
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 4013468
zbMATH Keywords: totally umbilical submanifold
zbMATH Keywords: CR-submanifold
zbMATH Keywords: totally real distribution
zbMATH Keywords: normal contact metric structure
zbMATH Keywords: parallel second fundamental form
Wikidata QID: Q115243304
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4013468