Rigidity of ergodic volume-preserving actions of semisimple groups of higher rank on compact manifolds
Author:
Guillaume Seydoux
Journal:
Trans. Amer. Math. Soc. 345 (1994), 753-776
MSC:
Primary 58F11; Secondary 57S20
DOI:
https://doi.org/10.1090/S0002-9947-1994-1250826-1
MathSciNet review:
1250826
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Abstract: Let M be a compact manifold, H a semisimple Lie group of higher rank (e.g., with
) and
an ergodic H-action on M which preserves a volume v. Such an H-action is conjectured to be "locally rigid": if
is a sufficiently
-small perturbation of a, then there should exist a diffeomorphism
of the manifold M which conjugates
to a. This conjecture would imply that if
is an a-invariant geometrical structure on M, then there should exist an.
-invariant geometrical structure
on M of the same type. Using Kazhdan property, superrigidity for cocycles, and Sobolev spaces techniques we prove, under suitable conditions, two such results with
and with
a Riemannian metric along the leaves of a foliation of M.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1994-1250826-1
Article copyright:
© Copyright 1994
American Mathematical Society