On the curvature of tensor product connections and covariant differentials

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Authors

JANYŠKA Josef

Year of publication 2004
Type Article in Periodical
Magazine / Source Supplemento di Rendiconti del Circolo Matematico di Palermo
MU Faculty or unit

Faculty of Science

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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