Enchev, Ognian; Strook, Daniel W. Towards a Riemannian geometry on the path space over a Riemannian manifold. (English) Zbl 0847.58080 J. Funct. Anal. 134, No. 2, 392-416 (1995). 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. Reviewer: S.Eloshvili (Tbilisi) Cited in 2 ReviewsCited in 29 Documents MSC: 58J65 Diffusion processes and stochastic analysis on manifolds 60J65 Brownian motion Keywords:Riemannian manifold; path space; Brownian motion PDFBibTeX XMLCite \textit{O. Enchev} and \textit{D. W. Strook}, J. Funct. Anal. 134, No. 2, 392--416 (1995; Zbl 0847.58080) Full Text: DOI