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Towards a Riemannian geometry on the path space over a Riemannian manifold. (English) Zbl 0847.58080

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.

MSC:

58J65 Diffusion processes and stochastic analysis on manifolds
60J65 Brownian motion
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