The degrees of the standard imbeddings of R-spaces
type: Item
instance of: scholarly article
title: The degrees of the standard imbeddings of R-spaces
zbMATH Open document ID: 0532.53041
author: Yoshihiro Ohnita
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1983-01-01T00:00:00Z
review text: The degree d of a (homogeneous) submanifold is the number of the highest non-vanishing fundamental form. Hence \(d=1\) means ''totally geodesic'', while ''parallel second fundamental form'' implies \(d\leq 2\). Main result: \(d=2\) for all standard embedded R-spaces.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 3844570
zbMATH Keywords: R-space
zbMATH Keywords: parallel second fundamental form
reviewed by: Dirk Ferus
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228946
OpenAlex ID: W2004335664
cites work: Symmetric submanifolds of Euclidean space
cites work: Q3897665
cites work: On the mean curvature of R-spaces
cites work: Degree of the standard isometric minimal immersions of complex projective spaces into spheres
cites work: Degree of the standard isometric minimal immersions of the symmetric spaces of rank one into spheres
cites work: Minimal imbeddings of R-spaces
cites work: Q5640359
DOI: 10.2748/TMJ/1178228946
description: scientific article; zbMATH DE number 3844570