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Basic differential forms
for actions of Lie groups

Author: Peter W. Michor
Journal: Proc. Amer. Math. Soc. 124 (1996), 1633-1642
MSC (1991): Primary 57S15, 20F55
MathSciNet review: 1307550
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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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Additional Information

Peter W. Michor
Affiliation: Erwin Schrödinger International Institute of Mathematical Physics, Wien, Austria, Institut für Mathematik, Universität Wien, Austria; Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria

Keywords: Orbits, sections, basic differential forms
Received by editor(s): April 6, 1994
Received by editor(s) in revised form: November 9, 1994
Additional Notes: Supported by Project P 10037–PHY of ‘Fonds zur Förderung der wissenschaftlichen Forschung’.
Communicated by: Roe W. Goodman
Article copyright: © Copyright 1996 American Mathematical Society

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