Geodesic
Transversal Lie jets and holomorphic geometric objects on transverse bundles
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2016), pp. 80-85 Cet article a éte moissonné depuis la source Math-Net.Ru

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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},
     year = {2016},
     number = {5},
     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/

[1] Molino P., Riemannian foliations, Birkhäuser, Boston, 1988 | MR | Zbl

[2] Weil A., “Théorie des points proches sur les variététes différentiables”, Colloque internat. centre nat. rech. sci. (Strasbourg), 52 (1953), 111–117 | MR | Zbl

[3] Kolář I., Michor P. W., Slovák J., Natural operations in differential geometry, Springer-Verlag, Berlin, 1993 | MR | Zbl

[4] Shurygin V. V., “Smooth manifolds over local algebras and Weil bundles”, J. Math. Sci., 108:2 (2002), 249–294 | DOI | MR | Zbl

[5] Shurygin V. V., “Mnogoobraziya nad algebrami i ikh primenenie v geometrii rassloenii strui”, UMN, 48:2 (1993), 75–106 | MR | Zbl

[6] Vishnevskii V. V., “Integriruemye affinornye struktury i ikh plyuralnye interpretatsii”, Itogi nauki i tekhn. Sovremen. matem. i ee prilozh., 73, VINITI, M., 2002, 5–64 | MR | Zbl

[7] Pogoda Z., “Horizontal lifts and foliations”, Rend. Circ. mat. Palermo. Ser. 2, 38, suppl. No 21 (1989), 279–289 | MR