Wirkungen von Lie Algebren und Lie Gruppen

Conjecture. Let G be a compact Lie group which acts isometrically on a complete Riemannian manifold M , such that this action admits a section: There exists a closed submanifold Σ in M which meets each orbit orthogonally. Then the space Ωhor(M) of all differential forms on M which are invariant under the G-action and are horizontal in the sense that they kill each vector which is tangent to an orbit, is isomorphic to the space Ω(Σ) (Σ) of all differential forms on the section Σ, which are invariant under the action of the Weyl group W (Σ) on Σ, where