The global structure of the geodesics on a complete Riemannian manifold
Lebrun, Claude Rene
Shalen, Peter B.
Master of Arts
Information is obtained concerning the large scale behavior of geodesics on Riemannian manifolds of certain broad types by studying the topology of certain fibrations used in conjunction with the tools of the calculus of variations in the large. It is demonstrated that any compact Riemannian manifold possesses a closed geodesic and that any two points on a complete Riemannian manifold not having the homotopy type of a point are joined by infinitely many geodesics.