Killing tensor fields on the standard sphere and spectra of \(SO(n+1)/SO(n-1)\times SO(2)\) and \(O(n+1)/O(n-1)\times O(2)\)
type: Item
instance of: scholarly article
title: Killing tensor fields on the standard sphere and spectra of \(SO(n+1)/SO(n-1)\times SO(2)\) and \(O(n+1)/O(n-1)\times O(2)\)
zbMATH Open document ID: 0534.53038
author: Takeshi Sumitomo
author: Kwoichi Tandai
published in: Osaka Journal of Mathematics
publication date: 1983-01-01T00:00:00Z
review text: The goal of this paper is to exhibit the eigen-space decomposition for the Laplacian of the Grassmann manifolds in the title (with their canonical Riemannian metrics) and to clarify their relation to the eigen- space decomposition of the Lichnerowicz operator on the standard sphere \((S^ n,g_ 0)\) when restricted to the symmetric tensor algebra generated by the Killing vector fields.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 3848183
zbMATH Keywords: Laplacian
zbMATH Keywords: Grassmann manifolds
zbMATH Keywords: eigen-space decomposition
zbMATH Keywords: Lichnerowicz operator
reviewed by: Oldřich Kowalski
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3848183