✦ LIBER ✦

Markovian Connection, Curvature and Weitzenböck Formula on Riemannian Path Spaces

✍ Scribed by Shizan Fang

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 212 KB
Volume: 181
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2000.3719

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✦ Synopsis

We shall consider on a Riemannian path space P m o (M ) the Cruzeiro Malliavin's Markovian connection. The Laplace operator will be defined as the divergence of the gradient. We shall compute explicitly the associated curvature tensor. A Weitzenbo ck formula will be established. To this end, we shall introduce an ``inner product'' between the tangent processes and simple vector fields.