Codimension of immersions with parallel pluri-mean curvature
type: Item
instance of: scholarly article
title: Codimension of immersions with parallel pluri-mean curvature
zbMATH Open document ID: 1180.53061
published in: Differential Geometry and its Applications
publication date: 2009-11-18T00:00:00Z
review text: An isometric immersion of a Kähler manifold in Euclidean space is said to have parallel pluri-mean curvature (`ppmc') if the \((1,1)\) part of its second fundamental form \(\alpha\) is parallel. Among the examples, there are the Hermitian symmetric spaces. In this paper, the authors show that these ones have the smallest codimension among all ppmc immersions, with the exception of the reducible Kähler manifolds.
reviewed by: Liviu Ornea
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53A07
zbMATH DE Number: 5634913
zbMATH Keywords: immersion
zbMATH Keywords: pluri-mean curvature
zbMATH Keywords: Kähler manifold
zbMATH Keywords: symmetric space
author: J.-H. Eschenburg
author: Andreas Kollross
author: R. Tribuzy
MaRDI profile type: Publication
full work available at URL: j.difgeo.2009.03.009
OpenAlex ID: W2092062164
Wikidata QID: Q115357273
cites work: Q4720334
cites work: Kähler submanifolds with parallel pluri-mean curvature.
cites work: Real Kaehler submanifolds and uniqueness of the Gauss map
cites work: Q3615741
cites work: Isotropic ppmc immersions
cites work: On the type decomposition of the second fundamental form of a Kähler submanifold
cites work: Symmetric submanifolds of Euclidean space
cites work: Q3897665
cites work: A geometric proof of the Berger holonomy theorem
cites work: On the transitivity of holonomy systems
cites work: Symmetric spaces and strongly isotropy irreducible spaces
DOI: 10.1016/J.DIFGEO.2009.03.009
description: scientific article; zbMATH DE number 5634913