The uniformly partially hyperbolic quasi-affine conjecture

Let $G$ be a semisimple Lie group all of whose simple factors have property $(T)$, and let $\Gamma<G$ be a lattice. Assume that $G$ or $\Gamma$ acts smoothly on a compact manifold $M$ preserving volume, and that some element $g$ of the acting group is non-trivially uniformly partially hyperbolic. The uniformly partially hyperbolic quasi-affine conjecture. The action should be generalized quasi-affine. This is a broad hyperbolic-action rigidity conjecture and remains open.