Smooth Factors of Projective Actions of Higher Rank Lattices and   Rigidity
  We study smooth factors of the standard actions of lattices in higher rank semisimple Lie groups on flag manifolds. Under a mild condition on existence of a single differentiable sink, we show that these factors are $C^{\infty}$-conjugate to the standard actions on flag manifolds. 
Alexander Gorodnik and Ralf Spatzier
math.DS