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Commutation relations on the covariant derivative

A. V. Gavrilov
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Abstract

The n-th order covariant derivative on a smooth manifold with an affine connection is a differential operator which turns a function into a tensor field of type (0,n). In this paper the properties of this operatior related to the permutation of indices are investigated by means of non-associative algebra. The general formula for commutation relations of this kind is obtained.

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A. V. Gavrilov. 2011-06-26. Commutation relations on the covariant derivative. https://arxiv.org/abs/math/0605041

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