Abstract
In this paper we prove higher order version of the Utiyama-like theorem. To prove the Utiyama-like theorem in order r ≥ 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 co-variant differentials, where the covariant differential of curvature tensors of principal connections is considered with respect to both connections.
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