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The Leibniz formula for the covariant derivative and some of its applications

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Abstract

We obtain a formula for the higher covariant derivatives on the tensor product of vector bundles which is a wide generalization of the classical Leibniz formula. We construct an algorithm for the calculation of the part of the Taylor series of the double exponential map linear with respect to the second variable.

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References

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Authors and Affiliations

  1. Siberian Independent Institute, Novosibirsk, 630082, Russia

    A. V. Gavrilov

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  1. A. V. Gavrilov
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Correspondence to A. V. Gavrilov.

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Original Russian Text © A. V. Gavrilov, 2010, published in Matematicheskie Trudy, 2010, Vol. 13, No. 1, pp. 63–84.

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Gavrilov, A.V. The Leibniz formula for the covariant derivative and some of its applications. Sib. Adv. Math. 22, 80–94 (2012). https://doi.org/10.3103/S1055134412020022

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  • DOI: https://doi.org/10.3103/S1055134412020022

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