Extrinsic hyperspheres of naturally reductive homogeneous spaces
type: Item
instance of: scholarly article
title: Extrinsic hyperspheres of naturally reductive homogeneous spaces
zbMATH Open document ID: 0881.53050
author: Koji Tojo
published in: Tokyo Journal of Mathematics
publication date: 1998-01-13T00:00:00Z
review text: A submanifold of a Riemannian manifold is called an extrinsic sphere if it is a totally umbilical submanifold with nonzero parallel mean curvature vector. It was proved in [\textit{B.-Y. Chen}, Mich. Math. J. 24, 265-271 (1977; Zbl 0389.53025)] that a locally symmetric space admits an \(n\)-dimensional extrinsic sphere if and only if it admits an \((n+1)\)-dimensional totally geodesic submanifold of constant sectional curvature. In this article, the author investigates a similar problem for naturally reductive homogeneous spaces and proves that if a naturally reductive homogeneous space admits an extrinsic hypersphere, then it is a space of constant sectional curvature.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 1054588
zbMATH Keywords: extrinsic sphere
zbMATH Keywords: naturally reductive homogeneous space
zbMATH Keywords: locally symmetric space
zbMATH Keywords: constant sectional curvature
reviewed by: Bang-Yen Chen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270042396
OpenAlex ID: W2080616303
DOI: 10.3836/TJM/1270042396
description: scientific article; zbMATH DE number 1054588