Higher order valued reduction theorems for general linear connections


The reduction theorems for general linear and classical connections are  generalized for operators with values in higher order gauge-natural bundles.  We prove that natural operators depending on the s_1-jets of classical  connections, on the s_2-jets of general linear connections and on the  r-jets of tensor fields with values in gauge-natural bundles of order k\ge 1, s_1+2\ge s_2, s_1,s_2\ge r-1\ge k-2, can be factorized through the  (k-2)-jets of both connections, the (k-1)-jets of the tensor fields and  sufficiently high covariant differentials of the curvature tensors and the  tensor fields.

DOI Code: 10.1285/i15900932v23n2p75

Keywords: Gauge-natural bundle; natural operator; Linear connection; Classical connection; Reduction theorem

Classification: 53C05; 58A20

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