Killing vector fields and the holonomy algebra in semiriemannian manifolds
type: Item
instance of: scholarly article
title: Killing vector fields and the holonomy algebra in semiriemannian manifolds
zbMATH Open document ID: 0694.53059
author: Enric Fossas i Colet
published in: Tsukuba Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: A well-known theorem of B. Kostant states that in case of compact Riemannian manifolds the operator \(A_ X:=L_ X-\nabla_ X\) lies in the holonomy algebra of the manifold. In this paper the author generalizes this result to compact semi-Riemannian manifolds. He also proves that on a compact homogeneous flat semi-Riemannian manifold any Killing vector field is parallel.
reviewed by: József Szilasi
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 4136940
zbMATH Keywords: holonomy algebra
zbMATH Keywords: semi-Riemannian manifolds
zbMATH Keywords: Killing vector field
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496161169
OpenAlex ID: W1497773463
DOI: 10.21099/TKBJM/1496161169
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description: scientific article; zbMATH DE number 4136940