Geodesic
Tangent bundles and gauge groups
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 3, pp. 249-263

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The differentials $T^ka$ $(k\ge1)$ of a diffeomorphism $a$ of a smooth manifold $M$ induce in the fibers of the fiber bundles $T^kM,$ i.e., in the corresponding tangent spaces, linear transformations, which embody the action of the gauge group $\mathcal G_k$. This action extends in a natural way to the osculating subbundles $\mathrm{Osc}^{k-1}M\subset T^kM$.
Keywords: diffeomorphism of a smooth manifold, fiber bundles, action of the gauge group. 
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     title = {Tangent bundles and gauge groups},
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M. Rahula; V. Balan. Tangent bundles and gauge groups. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 3, pp. 249-263. http://geodesic.mathdoc.fr/item/UZKU_2011_153_3_a23/