Abstract
We obtain a composition formula for the higher covariant derivatives on a vector bundle over a manifold. The formula generalizes the classical Leibniz product rule for the derivative. We also obtain, as a corollary, a generalization of the author’s theorem about the double exponential map to the case of multiple maps.
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Original Russian Text Copyright © 2008 Gavrilov A. V.
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Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 6, pp. 1250–1262, November–December, 2008.
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Gavrilov, A.V. Higher covariant derivatives. Sib Math J 49, 997–1007 (2008). https://doi.org/10.1007/s11202-008-0096-7
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DOI: https://doi.org/10.1007/s11202-008-0096-7