Weak Levi-Civita connection for the damped metric on the Riemannian path space and vanishing of Ricci tensor in adapted differential geometry (Q5952331)

The authors endow the path space over a compact manifold with some adapted Markovian connection \(\nabla\), which takes the curvature tensor into account, is not compatible with the Cameron-Martin metric, but is however compatible with another metric depending on the Ricci tensor (on which no hypothesis is made). The Ornstein-Uhlenbeck generator \({\mathcal L}\) associated with \(\nabla\) is computed, and a Weitzenböck formula is established for this operator \({\mathcal L}\).