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Frame Bundle of Riemannian Path Space and Ricci Tensor in Adapted Differential Geometry

✍ Scribed by Ana-Bela Cruzeiro; Paul Malliavin

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 280 KB
Volume: 177
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2000.3634

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✦ Synopsis

The vanishing of the renormalized Ricci tensor of the path space above a Ricci flat Riemannian manifold is discussed.

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Weak Levi-Civita Connection for the Damp

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

✍ Ana Bela Cruzeiro; Shizan Fang 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 154 KB

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