Towards a Riemannian geometry on the path space over a Riemannian manifold
Let \(M\) be a compact, connected, \(d\)-dimensional Riemannian manifold, and \({\mathcal P} (M)\) be the path space \(C([0,\infty); M)\), with the topology of uniform convergence on finite time intervals. The purpose of this article is to examine a Riemannian structure for \({\mathcal P}(M)\) with respect to which the distribution of the Brownian motion on \(M\) is a natural choice of smooth measure.
scientific article; zbMATH DE number 850627