We consider cocycles over certain hyperbolic ℝ k actions, k ≥ 2, and show rigidity properties for cocycles with values in a Lie group or a diffeomorphism group, which are close to identity on a set of generators, and are sufficiently smooth. The actions we consider are Cartan actions of SL(n,\ℝ)/Γ or SL(n,ℂ)/Γ, for n ≥ 3, and Γ torsion free cocompact lattice. The results in this paper rely on a technique developed recently by D. Damjanović and A. Katok.
All Science Journal Classification (ASJC) codes
- Geometry and Topology