Nonnegatively curved totally real submanifolds
type: Item
instance of: scholarly article
title: Nonnegatively curved totally real submanifolds
zbMATH Open document ID: 0562.53036
DOI: 10.1007/BF01451413
author: Francisco Urbano
published in: Mathematische Annalen
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164061
review text: Let M be an n-dimensional nonnegatively curved compact totally real submanifold of an n-dimensional Kähler manifold \(\bar M\) with parallel mean curvature vector. The main purpose of this paper is to classify these submanifolds when \(\bar M\) is the complex Euclidean, projective or hyperbolic space. For this, the author uses the classification of totally real parallel submanifolds in these spaces given by H. Naitoh and M. Takeuchi, and proves the following main result: ''Let M be an n- dimensional compact totally real submanifold of an n-dimensional complex space form with parallel mean curvature vector. If M has nonnegative sectional curvature, then M has parallel second fundamental form''.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 3895835
zbMATH Keywords: totally real submanifold
zbMATH Keywords: Kähler manifold
zbMATH Keywords: parallel mean curvature vector
zbMATH Keywords: nonnegative sectional curvature
MaRDI profile type: Publication
cites work: Symmetric submanifolds of Euclidean space
cites work: Parallel submanifolds of complex space forms I
cites work: Parallel submanifolds of complex space forms II
cites work: Totally real submanifolds and symmetric bounded domains
cites work: A characterization of seven compact Kähler submanifolds by holomorphic pinching
cites work: Totally Real Minimal Submanifolds of a Complex Projective Space
cites work: Submanifolds with Constant Mean Curvature
OpenAlex ID: W2065619455
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description: scientific article; zbMATH DE number 3895835