Let $ M $ be a hyperbolic manifold. If $ M $ has finite volume (this includes all compact hyperbolic manifolds of course) then no Lie group can act transitively on $ M $.
But what about geometrically finite hyperbolic manifolds? A hyperbolic manifold is called geometrically finite if the thick part of its convex core is compact.
Is it possible for a Lie group $ G $ to act transitively on a geometrically finite hyperbolic manifold $ M $?