Differential geometry of \(\mathfrak{g}\)-manifolds
type: Item
instance of: scholarly article
title: Differential geometry of \(\mathfrak{g}\)-manifolds
zbMATH Open document ID: 0854.53028
DOI: 10.1016/0926-2245(95)00023-2
published in: Differential Geometry and its Applications
publication date: 1997-01-22T00:00:00Z
review text: Let \(\mathfrak g\) be a finite-dimensional Lie algebra. A \(\mathfrak g\)-manifold is a manifold \(M\) with an action of \(\mathfrak g\), i.e. with an algebra homomorphism from \(\mathfrak g\) into the Lie algebra of all vector fields on \(M\). First of all, the authors consider the pseudogroup of all local transformations generated by an action of \(\mathfrak g\) and discuss its graph. If the orbits are equidimensional, many ideas from the theory of connections can be extended to the space of orbits. In such a situation, the authors study systematically the Frölicher-Nijenhuis bracket, curvature, covariant differentiation, Bianchi identity, parallel transport, basic differential forms, basic cohomology and characteristic classes.
Mathematics Subject Classification ID: 53C10
Mathematics Subject Classification ID: 53B05
zbMATH DE Number: 897459
zbMATH Keywords: \(\mathfrak g\)-manifold
zbMATH Keywords: connections
zbMATH Keywords: curvature
zbMATH Keywords: characteristic classes
author: Dmitri Alekseevsky
author: Peter W. Michor
MaRDI profile type: Publication
full work available at URL: 0926-2245(95)00023-2
OpenAlex ID: W2038745894
Wikidata QID: Q62597186
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reviewed by: Ivan Kolář
description: scientific article; zbMATH DE number 897459