Totally umbilical CR-submanifolds of a Kaehler manifold
type: Item
instance of: scholarly article
title: Totally umbilical CR-submanifolds of a Kaehler manifold
zbMATH Open document ID: 0607.53034
author: Sharief Deshmukh
author: S. I. Husain
published in: Kodai Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: It was proved [see the reviewer, Geometry of CR-submanifolds (1986; Zbl 0605.53001); Theorem 2.1, p. 43] that a totally umbilical CR-submanifold M of a Kaehler manifold N is either totally geodesic or totally real, or dim \(D^{\perp}=1\). In the last case, \textit{T. Toyonari} and \textit{H. Nemoto} [TRU Math. 21, 61-66 (1985; Zbl 0578.53039)] proved that M is a Sasakian manifold. The present authors prove that in case dim \(D^{\perp}=1\) M is isometric to an ordinary sphere or it is homothetic to a Sasakian manifold.
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 3982007
zbMATH Keywords: CR-submanifolds
zbMATH Keywords: Kaehler manifold
zbMATH Keywords: Sasakian manifold
reviewed by: Aurel Bejancu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138037271
OpenAlex ID: W2000159582
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DOI: 10.2996/KMJ/1138037271
description: scientific article; zbMATH DE number 3982007