Basic differential forms for actions of Lie groups

  title={Basic differential forms for actions of Lie groups},
  author={Erwin Schr{\"o}dinger International and Peter W. Michor},
The assumption in the main result of [2] is removed Let G be a Lie group which acts isometrically on a Riemannian manifold M . A section of the Riemannian G-manifold M is a closed submanifold Σ which meets each orbit orthogonally. In this situation the trace on Σ of the G-action is a discrete group action by the generalized Weyl group W (Σ) = NG(Σ)/ZG(Σ), where NG(Σ) := {g ∈ G : g.Σ = Σ} and ZG(Σ) := {g ∈ G : g.s = s for all s ∈ Σ}. A differential form φ ∈ Ω(M) is called G-invariant if g… CONTINUE READING
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