On the curvature of Riemannian submanifolds of codimension 2
type: Item
instance of: scholarly article
title: On the curvature of Riemannian submanifolds of codimension 2
zbMATH Open document ID: 0573.53028
author: Yoshio Agaoka
published in: Hokkaido Mathematical Journal
publication date: 1985-01-01T00:00:00Z
review text: Let M be an n-dimensional Riemannian manifold which is isometrically immersed into some Euclidean space \(E^{n+k}\) with codimension k, and let R denote the curvature tensor of M. Then the Gauss equation implies \[ (*)\quad rank R(x,y)\leq 2k \] for all tangent vectors \(x,y\in T_ pM\), \(p\in M\). The purpose of the paper under review is to determine polynomial relations of the curvature tensor R and to find new conditions on R which may serve as obstructions similar to (*). One of the given applications is: SU(3)/SO(3) cannot be isometrically immersed with codimension 2 in Euclidean space, even locally. The method used is representation theory of GL(n,\({\mathbb{R}})\). Since the required calculations are lengthy and complicated the author makes use of an algebraic programming system in many places of the paper.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53A07
zbMATH DE Number: 3915154
zbMATH Keywords: isometric immersion
zbMATH Keywords: Young tableaux
zbMATH Keywords: curvature tensor
zbMATH Keywords: algebraic programming system
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381757683
OpenAlex ID: W2029050587
Wikidata QID: Q115237726
DOI: 10.14492/HOKMJ/1381757683
description: scientific article; zbMATH DE number 3915154