Basic differential forms for actions of Lie groups

Details Basic differential forms for actions of Lie groups Basic differential forms for actions of Lie groups

1994-06-30

arxiv.org/abs/dg-ga/9406006v1

Proc. AMS 124,5 (1996), 1633-1642

Mathematics

Differential Geometry

10 pages, ESI Preprint 87, AmSTeX

Scientific paper

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 this orbit, under some condition.

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