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Basic differential forms for actions of Lie groups

Peter W. Michor
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Abstract

A section of a Riemannian $G$-manifold $M$ is a closed submanifold $Σ$ which meets each orbit orthogonally. It is shown that the algebra of $G$-invariant differential forms on $M$ 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 $Σ$ which are invariant with respect to the generalized Weyl group of this orbit, under some condition.

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Peter W. Michor. 1994-06-30. Basic differential forms for actions of Lie groups. https://arxiv.org/abs/dg-ga/9406006

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