Local Rigidity of Higher Rank Homogeneous Abelian Actions: a Complete Solution via the Geometric Method

Kurt Vinhage, Zhenqi Jenny Wang

We show local and cocycle rigidity for ${\mathbb{R}}^k\times {\mathbb{Z}}^l$ partially hyperbolic translation actions on homogeneous spaces $\mc G/ Λ$. We consider a large class of actions whose geom…