On the curvature of tensor product connections and covariant differentials
| Authors | |
|---|---|
| Year of publication | 2004 |
| Type | Article in Periodical |
| Magazine / Source | Supplemento di Rendiconti del Circolo Matematico di Palermo |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | linear connection; curvature; covariant differential |
| Description | We give coordinate formula and geometric description of the curvature of the tensor product connection of linear connections on vector bundles with the same base manifold. We define the covariant differential of geometric fields of certain types with respect to a pair of a linear connection on a vector bundle and a linear symmetric connection on the base manifold. We prove the generalized Bianchi identity for linear connections and we prove that the antisymmetrization of the second order covariant differential is expressed via the curvature tensors of both connections. |
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