Markovian connection, curvature and Weitzenbock formula on Riemannian path spaces

摘要

We shall consider on a Riemannian path space P-m (M) the Cruzeiro-Malliavin's Markovian connection. The Laplace operator will be defined as the divergence of the gradient. We shall compute explicitly the associated curvature tensor. A Weitzenbock formula will be established. To this end, we shall introduce an "inner product" between the tangent processes and simple vector fields. (C) 2001 Academic Press. [References: 11]