  This work presents a framework for billiards in convex domains on two
dimensional Riemannian manifolds. These domains are contained in connected,
simply connected open subsets which are totally normal. In this context, some
basic properties that have long been known for billiards on the plane are
established. We prove the twist property and investigate conditions on the
billiard for the existence and non existence of rotational invariant curves.

Dynamical Systems