A Class of Vector Fields on Path Spaces

Authors: Lyons T.J.; Qian Z.M.

Source: Journal of Functional Analysis, Volume 145, Number 1, April 1997 , pp. 205-223(19)

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Abstract:

In this paper we show that the vector field X [inverted triangle],? h on a based path space W o ( M ) over a Riemannian manifold M defined by parallel translating a curve h in the initial tangent space T o M via an affine connection [inverted triangle] induces a solution flow which preserves the Wiener measure on the based path space W o ( M ), provided the affine connection [inverted triangle] is adjoint skew-symmetric. In the case when [inverted triangle] is a metric connection, then [inverted triangle] is adjoint skew-symmetric if and only if [inverted triangle] is torsion skew-symmetric.

Language: English

Document Type: Research article

Affiliations: Department of Mathematics, Imperial College of Science, Technology and Medicine, Huxley Building, 180 Queen's Gate, London, SW7 2BZ, United Kingdom

Publication date: 1997-04-01