Geodesic
Holomorphic Affine Vector Fields on Weil Bundles
Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 896-899

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain necessary and sufficient conditions for a holomorphic vector field to be affine for a holomorphic linear connection defined on a Weil bundle. We also prove that the Lie algebra over $\mathbb{R}$ of holomorphic affine vector fields for the natural prolongation of a linear connection from the base to the Weil bundle is isomorphic to the tensor product of the Weil algebra by the Lie algebra of affine vector fields on the base.
Mots-clés : Weil algebra, affine structure, prolongation of connections.
Keywords: Weil bundle, holomorphic vector field, holomorphic connection, affine vector field 
@article{MZM_2012_91_6_a9,
     author = {A. Ya. Sultanov},
     title = {Holomorphic {Affine} {Vector} {Fields} on {Weil} {Bundles}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {896--899},
     publisher = {mathdoc},
     volume = {91},
     number = {6},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a9/}
}
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A. Ya. Sultanov. Holomorphic Affine Vector Fields on Weil Bundles. Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 896-899. http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a9/