CR submanifolds of maximal CR dimension of complex projective space
type: Item
instance of: scholarly article
title: CR submanifolds of maximal CR dimension of complex projective space
zbMATH Open document ID: 0907.53039
author: Masafumi Okumura
author: Mirjana Djoric
published in: Archiv der Mathematik
publication date: 1999-02-18T00:00:00Z
review text: Let \(N\) be a Kähler manifold and \(M\) be a CR submanifold of \(N\) [cf. \textit{A. Bejancu}, `Geometry of CR-submanifolds' (Math. Appl. East Eur. Ser. 23, Kluwer, Dordrecht) (1986; Zbl 0605.53001)]. In the case that the totally real distribution on \(M\) is 1-dimensional, that is, \(M\) has maximal CR dimension, the authors obtain generalizations of some results from the theory of real hypersurfaces of \(N\). As an example, this generalizes a theorem stated by \textit{T. E. Cecil} and \textit{P. J. Ryan} [Trans. Am. Math. Soc. 269, 481-499 (1982; Zbl 0492.53039)] with respect to real hypersurfaces of \(N\) with at most two distinct principal curvatures at each point.
reviewed by: Aurel Bejancu
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 1214019
zbMATH Keywords: CR submanifold
zbMATH Keywords: shape operator
zbMATH Keywords: principal curvature
MaRDI profile type: Publication
full work available at URL: s000130050246
OpenAlex ID: W2073592388
DOI: 10.1007/S000130050246
description: scientific article; zbMATH DE number 1214019