Existence and uniqueness of geodesics on path spaces
The paper includes the proof of the global existence and the global uniqueness (in the class of Brownian semimartingales) of the geodesics with respect to an adapted Markovian connection on the path space over a compact Riemannian manifold. It is shown as well that the Wiener measure is quasi-invariant under the geodesic transformation.
scientific article; zbMATH DE number 1462831