A class of vector fields on path spaces (Q1354621)

The authors show that the vector field \(X^{\nabla,h}\) on a based path space \(W_0(M)\) over a Riemannian manifold \(M\) defined by parallel translating a curve \(h\) in the initial tangent space \(T_0M\) via an affine connection \(\nabla\) induces a solution flow which preserves the Wiener measure on the based path space \(W_0(M)\), provided the affine connection \(\nabla\) is adjoint skew-symmetric.