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@article{549384,
author = {Janyška, Josef},
article_location = {Amsterdam},
article_number = {2},
keywords = {Gauge-natural bundle; natural operator; linear connection; reduction theorem},
language = {eng},
issn = {0926-2245},
journal = {Differential Geometry and its Applications},
title = {Reduction theorems for general linear connections},
volume = {20},
year = {2004}
}
TY - JOUR
ID - 549384
AU - Janyška, Josef
PY - 2004
TI - Reduction theorems for general linear connections
JF - Differential Geometry and its Applications
VL - 20
IS - 2
SP - 177-196
EP - 177-196
PB - Elsevier Science
SN - 09262245
KW - Gauge-natural bundle
KW - natural operator
KW - linear connection
KW - reduction theorem
N2 - It is well known that natural operators of linear symmetric connections on manifolds and of classical tensor fields can be factorized through the curvature tensors, the tensor fields and their covariant differentials. We generalize this result for general linear connections on vector bundles. In this gauge-natural situation we need an auxiliary linear symmetric connection on the base manifold. We prove that natural operators defined on the spaces of general linear connections on vector bundles, on the spaces of linear symmetric connections on base manifolds and on certain tensor bundles can be factorized through the curvature tensors of linear and classical connections, the tensor fields and their covariant differentials with respect to both connections.
ER -
JANYŠKA, Josef. Reduction theorems for general linear connections. \textit{Differential Geometry and its Applications}. Amsterdam: Elsevier Science, 2004, vol.~20, No~2, p.~177-196. ISSN~0926-2245.
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