Higher order Utiyama-like theorem
| Authors | |
|---|---|
| Year of publication | 2006 |
| Type | Article in Periodical |
| Magazine / Source | REPORTS ON MATHEMATICAL PHYSICS |
| MU Faculty or unit | |
| Citation | |
| Web | http://www.elsevier.com/wps/find/journaldescription.cws_home/416/description#description |
| Field | General mathematics |
| Keywords | Gauge-natural bundle; natural operator; principal bundle; principal connection; Utiyama-like theorem; reduction theorem |
| Description | 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. |
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