Hopf rigidity for convex billiards on the hemisphere and hyperbolic   plane
  This paper deals with Hopf type rigidity for convex billiards on surfaces of constant curvature. We prove that the only convex billiard without conjugate points on the Hyperbolic plane or on the Hemisphere is circular billiard. 
Michael (Misha) Bialy
math.DG math.DS nlin.SI