✦ LIBER ✦

Weak Levi-Civita Connection for the Damped Metric on the Riemannian Path Space and Vanishing of Ricci Tensor in Adapted Differential Geometry

✍ Scribed by Ana Bela Cruzeiro; Shizan Fang

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 154 KB
Volume: 185
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2001.3765

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✦ Synopsis

We shall establish in the context of adapted differential geometry on the path space P mo (M) a Weitzenböck formula which generalizes that in (A. B. Cruzeiro and P. Malliavin, J. Funct. Anal. 177 (2000), 219-253), without hypothesis on the Ricci tensor. The renormalized Ricci tensor will be vanished. The connection introduced in (A.