6533b82efe1ef96bd1292813
RESEARCH PRODUCT
Markovian Connection, Curvature and Weitzenböck Formula on Riemannian Path Spaces
Shizan Fangsubject
Riemann curvature tensorCurvature of Riemannian manifoldsMathematical analysisConnection (mathematics)symbols.namesakeLaplace–Beltrami operatorsymbolsCurvature formSectional curvatureMathematics::Differential GeometryAnalysisRicci curvatureMathematicsScalar curvaturedescription
Abstract We shall consider on a Riemannian path space P m o ( M ) the Cruzeiro–Malliavin's Markovian connection. The Laplace operator will be defined as the divergence of the gradient. We shall compute explicitly the associated curvature tensor. A Weitzenbock formula will be established. To this end, we shall introduce an “inner product” between the tangent processes and simple vector fields.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2001-04-01 | Journal of Functional Analysis |