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Leafwise cohomology and rigidity of certain Lie group actions

Published online by Cambridge University Press:  02 December 2003

S. MATSUMOTO  and
Y. MITSUMATSU
S. MATSUMOTO
Affiliation:
Department of Mathematics, College of Science and Technology, Nihon University, 1-8 Kanda, Surugadai, Chiyoda-ku Tokyo 101-8308, Japan (e-mail: [email protected])
Y. MITSUMATSU
Affiliation:
Department of Mathematics, Faculty of Science and Technology, Chuo University, 1-13-27 Kasuga, Bunkyo-ku Tokyo 112-8551, Japan (e-mail: [email protected])
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Abstract

A locally free Lie group action on a closed manifold is called parameter rigid, if given another action with the same orbit foliation, there is a $C^\infty$ orbit-preserving diffeomorphism which conjugates one action to the other, up to an automorphism of the Lie group. We show some relationships between parameter rigidity and the first leafwise cohomology of the orbit foliation, and give a new example of a parameter rigid solvable group action. We also compute the first leafwise cohomology of the stable foliation of geodesic flows of closed orientable surfaces of constant negative curvature.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 6 , December 2003 , pp. 1839 - 1866
Copyright
2003 Cambridge University Press

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