The Structure of the Value Function in Pursuit-Evasion Games on Surfaces of Revolution

The paper studies pursuit-evasion games when a game space is a manifold different from a Euclidian space. In this case, there are two or more geodesy lines of equal length that connect players. Games on 2D surfaces are examined. New results for the games on hyperboloids are presented. An important role is played by focal points in a variational problem on geodesic line.