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A Class of Vector Fields on Path Spaces

✍ Scribed by T.J. Lyons; Z.M. Qian

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
366 KB
Volume
145
Category
Article
ISSN
0022-1236

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✦ Synopsis

In this paper we show that the vector field X {, 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 { induces a solution flow which preserves the Wiener measure on the based path space W o (M), provided the affine connection { is adjoint skew-symmetric. In the case when { is a metric connection, then { is adjoint skew-symmetric if and only if { is torsion skew-symmetric.

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