Change-of-variables formulas in Feynman integrals over trajectories in compact Riemannian manifolds. (Q1432633)

For Feynman path integrals in compact Riemannian manifolds, the authors derive formulae for logarithmic derivatives of pseudomeasures, i.e., integration by parts formula. And they also present formulae of the Feynman and Feynman-Kac types for solutions to Schrödinger equation on compact Riemannian manifolds. The basic role is played by the Feynman analogues of surface measures of another type which was introduced by the first author.