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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Email: MICHOR@ESI.AC.AT

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03195-4
PII: S 0002-9939(96)03195-4
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