Connection between non-metric differential geometry and mathematical theory of imperfections

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