Geodesically complete Lagrangians on manifolds

Abstract

In this paper we prove the “Geodesic Connectivity” of a large class of Lagrangian Functions defined on a differentiable manifold. The study is carried on by means of “Convex neighborhoods” of suitable associated “Finsler Metrics”. Hence, these metrics are useful to solve the problem considered here, too. This result strengthens the conjecture, once considered very promising and now almost forgotten, that the use of “Finsler Metrics” simplify the study of Lagrangian Functions.

Keywords

• lagrangian functions
• convex neighborhood
• geodesic connectivity