Search results for "Lanczos tensor"

showing 2 items of 2 documents

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

2001

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.

Weyl tensorRiemann curvature tensorCurvature of Riemannian manifoldsMathematical analysisRicci flowsymbols.namesakeLanczos tensorsymbolsRicci decompositionTensor densityRicci curvatureAnalysisMathematical physicsMathematicsJournal of Functional Analysis
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Ricci Tensors on Some Infinite Dimensional Lie Algebras

1999

Abstract The Ricci tensor has been computed in several infinite dimensional situations. In this work, we shall be interested in the case of the central extension of loop groups and in the asymptotic behaviour of the Ricci tensor on free loop groups as the Riemannian metric varies.

Weyl tensorPure mathematicsRiemann curvature tensorCurvature of Riemannian manifoldsMathematical analysisRicci flowEinstein tensorsymbols.namesakeLanczos tensorsymbolsRicci decompositionMathematics::Differential GeometryRicci curvatureAnalysisMathematicsJournal of Functional Analysis
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