Geodesic
Transversal Lie jets and holomorphic geometric objects on transverse bundles
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2016), pp. 80-85

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

Two holomorphic fields of geometric objects on a transverse Weil bundle are called equivalent if there exists a holomorphic diffeomorphism of this bundle onto itself which induces the identity transformation of the base manifold and maps one of these fields into the other. In terms of transverse Lie jets, we establish necessary and sufficient conditions for a holomorphic field of geometric objects on a transverse Weil bundle to be equivalent to the prolongation of a field of foliated geometric objects given on the base manifold. As an example, we consider a holomorphic linear connection on a transverse bundle.
Mots-clés : Weil algebra, Lie jet
Keywords: geometric object, Weil bundle, transverse bundle. 
@article{IVM_2016_5_a6,
     author = {S. K. Zubkova and V. V. Shurygin},
     title = {Transversal {Lie} jets and holomorphic geometric objects on transverse bundles},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {80--85},
     publisher = {mathdoc},
     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_5_a6/}
}
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S. K. Zubkova; V. V. Shurygin. Transversal Lie jets and holomorphic geometric objects on transverse bundles. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2016), pp. 80-85. http://geodesic.mathdoc.fr/item/IVM_2016_5_a6/