Basic differential forms for actions of Lie groups II.
Differential Geometry
2016-09-06 v1 Representation Theory
Abstract
The assumption in the main result of [Peter W. Michor: Basic Differential Forms for Actions of Lie Groups, Proc. AMS 124, 5 (1996) 1633-1642] is removed. Thus: A section of a Riemannian -manifold is a closed submanifold which meets each orbit orthogonally. It is shown that the algebra of -invariant differential forms on which are horizontal in the sense that they kill every vector which is tangent to some orbit, is isomorphic to the algebra of those differential forms on which are invariant with respect to the generalized Weyl group of , without any further condition.
Cite
@article{arxiv.math/9506223,
title = {Basic differential forms for actions of Lie groups II.},
author = {Peter W. Michor},
journal= {arXiv preprint arXiv:math/9506223},
year = {2016}
}