On the quasi-invariance of the Wiener measure on path spaces and the anticipative integrals over a Riemannian manifold

Some parts of stochastic analysis on curved spaces are revisted. A concise proof of the quasi-invariance of the Wiener measure on the path spaces over a Riemannian manifold is presented. The shifts are allowed to be in the Cameron-Martin space and random. The second part of the paper presents some remarks on the anticipative integrals on Riemannian manifolds.