6533b7d4fe1ef96bd1262ae6
RESEARCH PRODUCT
Weak Levi-Civita Connection for the Damped Metric on the Riemannian Path Space and Vanishing of Ricci Tensor in Adapted Differential Geometry
Shizan FangAna Bela Cruzeirosubject
Weyl tensorRiemann curvature tensorCurvature of Riemannian manifoldsMathematical analysisRicci flowsymbols.namesakeLanczos tensorsymbolsRicci decompositionTensor densityRicci curvatureAnalysisMathematical physicsMathematicsdescription
Abstract We shall establish in the context of adapted differential geometry on the path space P m o ( M ) a Weitzenbock 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. B. Cruzeiro and S. Fang, 1997, J. Funct. Anal. 143 , 400–414) will play a central role.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2001-10-01 | Journal of Functional Analysis |