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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, roč.~20, č.~2, s.~177-196. ISSN~0926-2245.
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