Basic differential forms for actions of Lie groups

Michor, Peter

doi:10.1090/S0002-9939-96-03195-4

Basic differential forms for actions of Lie groups
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by Peter W. Michor PDF

Proc. Amer. Math. Soc. 124 (1996), 1633-1642 Request permission

Abstract:

A section of a Riemannian $G$-manifold $M$ is a closed submanifold $\Sigma$ 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 $\Sigma$ which are invariant with respect to the generalized Weyl group of $\Sigma$, under some condition.

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