  This paper provides a geometrical derivation of the Hybrid Minimum Principle
(HMP) for autonomous impulsive hybrid systems on Riemannian manifolds, i.e.
systems where the manifold valued component of the hybrid state trajectory may
have a jump discontinuity when the discrete component changes value. The
analysis is expressed in terms of extremal trajectories on the cotangent bundle
of the manifold state space. In the case of autonomous hybrid systems,
switching manifolds are defined as smooth embedded submanifolds of the state
manifold and the jump function is defined as a smooth map on the switching
manifold. The HMP results are obtained in the case of time invariant switching
manifolds and state jumps on Riemannian manifolds.
