\(A_ X\)-operator on complete Riemannian manifolds
type: Item
instance of: scholarly article
title: \(A_ X\)-operator on complete Riemannian manifolds
zbMATH Open document ID: 0602.53032
DOI: 10.1007/BF02786564
author: Carlos Currás-Bosch
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: In a Riemannian manifold (M,g), let \(L_ X\) and \(\nabla_ X\) be the Lie and covariant derivations with respect to a Killing vector field X. Then \(A_ X=L_ X-\nabla_ X\) is a skew-symmetric operator field. B. Kostant proved that \(A_ X\) belongs to the holonomy algebra at each point, if M is compact. The present author proves that this fact is also true in a complete non-compact (M,g), under the assumption that X has a finite global norm.
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 3971665
zbMATH Keywords: global scalar product
zbMATH Keywords: Killing vector field
zbMATH Keywords: holonomy algebra
zbMATH Keywords: finite global norm
Wikidata QID: Q115391635
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02786564
OpenAlex ID: W2069403341
description: scientific article; zbMATH DE number 3971665