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Higher order reduction theorems for general linear connections

Josef Janyška
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Abstract

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.

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Josef Janyška. 2004-05-26. Higher order reduction theorems for general linear connections. https://arxiv.org/abs/math/0405488

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