A Simple Pursuit–Evasion Problem on a Ball of a Riemannian Manifold

A pursuit–evasion differential game with simple motions, in which points (players) move on a ball of a Riemannian manifold, is studied. It is assumed that all players have the same dynamic capabilities, pursuers move on the entire ball, and evaders move either on the sphere bounding the ball or on the entire ball, depending on the version of the game. Sufficient solvability conditions are found. An example is given.