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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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