Commutation relations on the covariant derivative

Research paper by A. V. Gavrilov

Indexed on: 26 Jun '11Published on: 26 Jun '11Published in: Mathematics - Differential Geometry


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.