On the Classification of Cartan Actions
  We study higher rank Cartan actions on compact manifolds preserving an ergodic measure with full support. In particular, we classify actions by $\R ^k$ with $k \geq 3$ whose one-parameter groups act transitively as well as nondegenerate totally nonsymplectic $\Zk$-actions for $k \geq 3$. 
Boris Kalinin and Ralf Spatzier