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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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