A Girsanov Theorem in Manifolds and Projective Maps

Our purpose is to show a version of Girsanov theorem in smooth manifolds. After, we will use it theorem to give stochastic characterization for strongly projective maps. This stochastic characterization yields a proof that projective maps of rank $\geq 2$ between Riemannian manifolds, with connected domain, are affine maps. In particular, the groups of affine and projective transformations, in connected Riemannian manifold, are equal.