Geodesic
The Leibniz formula for the covariant derivative and some of its applications
Matematičeskie trudy, Tome 13 (2010) no. 1, pp. 63-84 
A. V. Gavrilov. The Leibniz formula for the covariant derivative and some of its applications. Matematičeskie trudy, Tome 13 (2010) no. 1, pp. 63-84. http://geodesic.mathdoc.fr/item/MT_2010_13_1_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Gavrilov A. V., “Algebraicheskie svoistva kovariantnogo differentsirovaniya i kompozitsiya eksponentsialnykh otobrazhenii”, Mat. trudy, 9:1 (2006), 3–20 | MR

[2] Gavrilov A. V., “Dvoinoe eksponentsialnoe otobrazhenie i kovariantnoe differentsirovanie”, Sib. mat. zhurn., 48:1 (2007), 68–74 | MR | Zbl

[3] Gavrilov A. V., “O vysshikh kovariantnykh proizvodnykh”, Sib. mat. zhurn., 49:6 (2008), 1250–1262 | MR

[4] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, v. 1–2, Nauka, M., 1981

[5] Sharafutdinov V. A., “Geometricheskoe ischislenie simvolov psevdodifferentsialnykh operatorov. I”, Mat. trudy, 7:2 (2004), 159–206 ; “II”, 8:1 (2005), 176–201 | MR | Zbl | MR | Zbl

[6] Gavrilov A. V., “Commutation relations on the covariant derivative”, J. Algebra, 323:2 (2010), 517–521 | DOI | MR | Zbl

[7] Montgomery S., Hopf Algebras and Their Actions on Rings, CBMS Regional Conf. Ser. Math., 82, Amer. Math. Soc., Providence, RI, 1993 | MR | Zbl