Homogeneous submanifolds of higher rank and parallel mean curvature
type: Item
instance of: scholarly article
title: Homogeneous submanifolds of higher rank and parallel mean curvature
zbMATH Open document ID: 0806.53054
published in: Journal of Differential Geometry
publication date: 1995-02-19T00:00:00Z
review text: The purpose of this article is to investigate the following problem: When is a homogeneous submanifold of a Euclidean space an orbit of the isotropy representation of a simple symmetric space? The author proves the following results in this respect. Theorem 1. If \(M^ n\), \(n \geq 2\), is a compact homogeneous irreducible full submanifold of the Euclidean space with rank \((M^ n) \geq 2\), then \(M^ n\) is an orbit of the isotropy representation of a simple symmetric space. Theorem 2. If \(M^ n\) is a compact homogeneous irreducible submanifold of the Euclidean space with parallel mean curvature vector which is not minimal in a sphere, then \(M^ n\) is an orbit of the isotropy representation of a simple symmetric space. By the rank of a submanifold the author means the maximal number of linearly independent (locally defined) parallel normal vector fields.
reviewed by: Bang-Yen Chen
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 606997
zbMATH Keywords: homogeneous submanifold
zbMATH Keywords: isotropy representation
zbMATH Keywords: simple symmetric space
zbMATH Keywords: parallel mean curvature vector
author: Carlos Olmos
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214455074
OpenAlex ID: W1579134133
Wikidata QID: Q115179588
DOI: 10.4310/JDG/1214455074
description: scientific article; zbMATH DE number 606997