Existence and Uniqueness of Geodesics on Path Spaces

Abstract

We prove the global existence and the global uniqueness (in the class of Brownian semimartingales) of the geodesic with respect to an adapted Markovian connection on the path space over a compact Riemannian manifold. The Wiener measure is proved to be quasi-invariant under the geodesic transformation. © 2000 Academic Press.