Towards a Riemannian geometry on the path space over a Riemannian manifold
type: Item
instance of: scholarly article
title: Towards a Riemannian geometry on the path space over a Riemannian manifold
zbMATH Open document ID: 0847.58080
published in: Journal of Functional Analysis
publication date: 1996-03-04T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 850627
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: path space
zbMATH Keywords: Brownian motion
author: Andrew Lyasoff
author: Daniel W. Stroock
reviewed by: Simon Eloshvili
MaRDI profile type: Publication
full work available at URL: jfan.1995.1151
OpenAlex ID: W2031609484
DOI: 10.1006/JFAN.1995.1151
description: scientific article; zbMATH DE number 850627