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@article{553759, author = {Janyška, Josef}, article_location = {Palermo}, article_number = {1}, keywords = {linear connection; curvature; covariant differential}, language = {eng}, issn = {0009-725X}, journal = {Supplemento di Rendiconti del Circolo Matematico di Palermo}, title = {On the curvature of tensor product connections and covariant differentials}, volume = {72}, year = {2004} }
TY - JOUR ID - 553759 AU - Janyška, Josef PY - 2004 TI - On the curvature of tensor product connections and covariant differentials JF - Supplemento di Rendiconti del Circolo Matematico di Palermo VL - 72 IS - 1 SP - 135-143 EP - 135-143 SN - 0009725X KW - linear connection KW - curvature KW - covariant differential N2 - 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. ER -
JANYŠKA, Josef. On the curvature of tensor product connections and covariant differentials. \textit{Supplemento di Rendiconti del Circolo Matematico di Palermo}. Palermo, 2004, vol.~72, No~1, p.~135-143. ISSN~0009-725X.
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