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@article{694454, author = {Janyška, Josef}, article_number = {1}, keywords = {Gauge-natural bundle; natural operator; principal bundle; principal connection; Utiyama-like theorem; reduction theorem}, language = {eng}, issn = {0034-4877}, journal = {REPORTS ON MATHEMATICAL PHYSICS}, title = {Higher order Utiyama-like theorem}, url = {http://www.elsevier.com/wps/find/journaldescription.cws_home/416/description#description}, volume = {58}, year = {2006} }
TY - JOUR ID - 694454 AU - Janyška, Josef PY - 2006 TI - Higher order Utiyama-like theorem JF - REPORTS ON MATHEMATICAL PHYSICS VL - 58 IS - 1 SP - 93-118 EP - 93-118 PB - Elsevier SAS SN - 00344877 KW - Gauge-natural bundle KW - natural operator KW - principal bundle KW - principal connection KW - Utiyama-like theorem KW - reduction theorem UR - http://www.elsevier.com/wps/find/journaldescription.cws_home/416/description#description N2 - In this paper we prove higher order version of the Utiyama-like theorem. To prove the Utiyama-like theorem in order $r\ge 2$ we have to use auxiliary classical connections on base manifolds. We prove that any natural (invariant) operator of order $r$ for principal connections on principal $G$-bundles and for classical connections on base manifolds with values in a $(1,0)$-order $G$-gauge-natural bundle factorizes through curvature tensors of both connections and their covariant differentials, where the covariant differential of curvature tensors of principal connections is considered with respect to both connections. ER -
JANYŠKA, Josef. Higher order Utiyama-like theorem. \textit{REPORTS ON MATHEMATICAL PHYSICS}. Elsevier SAS, 2006, roč.~58, č.~1, s.~93-118. ISSN~0034-4877.
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