On the symplectic structure of the space of geodesics of a Hadamard manifold (Q1376487)

A Hadamard manifold is a simply connected manifold endowed with a complete Riemannian metric with negative or null sectional curvature. The author proves that the space of geodesics of a Hadamard manifold of dimension \(n\) is symplectomorphic to the cotangent bundle of the sphere of dimension \(n-1\). A generalization to Finsler metrics and an application to wave fronts are pointed out.