Totally real submanifolds in a 6-sphere
type: Item
instance of: scholarly article
title: Totally real submanifolds in a 6-sphere
zbMATH Open document ID: 0754.53041
author: Sharief Deshmukh
published in: Michigan Mathematical Journal
publication date: 1992-09-27T00:00:00Z
review text: Consider the 6-dimensional Riemannian sphere \(S^ 6\) with constant curvature 1 endowed with the nearly Kähler structure induced from the Cayley divison algebra. Suppose that \(M\) is a 3-dimensional compact totally real submanifold of \(S^ 6\) and let \(k_ 0\) be the infimum of the sectional curvature of \(M\). The author proves that either \(4k_ 0\leq 1\) or \(M\) is totally geodesic.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 59879
zbMATH Keywords: curvature bound
zbMATH Keywords: nearly Kähler structure
zbMATH Keywords: Cayley divison algebra
reviewed by: Jürgen Berndt
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029004387
OpenAlex ID: W1992638299
DOI: 10.1307/MMJ/1029004387
description: scientific article; zbMATH DE number 59879