Games of simple pursuit and approach on the manifolds (Q1337004)

Pursuit-evasion games, in which the pursuer has a maximum speed advantage, which the speed constraints remain homogeneous, are considered. Minimal geodesic curves will then connect any two points on the manifold. A solution for the case of manifolds having no more than two minimal geodesic curves is presented; this solution grants the player's regular motion along geodesics. Then follows a derivation of optimality conditions. A four-step algorithm, for the construction of solutions close to the boundary manifold is provided. The specific case of games on the cone is discussed.