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Transverse Lie jets and holomorphic geometric objects on transverse bundles

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Abstract

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.

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References

  1. Molino, P. Riemannian Foliations (Birkhäuser, Boston, 1988).

    Book  MATH  Google Scholar 

  2. Weil, A. “Théorie des Points Proches sur les Variététes Différentiables”, Colloque internat. centre nat. rech. sci. 52 (Strasbourg, 1953), 111–117 (1953).

    MathSciNet  Google Scholar 

  3. Kolář, I., Michor, P. W., and Slovák, J. Natural Operations in Differential Geometry (Springer-Verlag, Berlin, 1993).

    Book  MATH  Google Scholar 

  4. Shurygin, V. V. “Smooth Manifolds over Local Algebras and Weil Bundles”, J. Math. Sci. 108 (2), 249–294 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  5. Shurygin, V. V. “Manifolds over Algebras and Their Application to the Geometry of Jet Bundles”, Russ. Math. Surv. 48 (2), 75–104 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  6. Vishnevskii, V. V. “Integrable Affinor Structures and Their Plural Interpretations”, J. Math. Sci. (New York) 108 (2002), No. 2, 151–187 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  7. Pogoda, Z. “Horizontal Lifts and Foliations”, Rend. Circ. mat. Palermo. Ser. 2, 38, suppl. No. 21, 279–289 (1989).

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Kazan (Volga Region) Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    S. K. Zubkova & V. V. Shurygin

Authors
  1. S. K. Zubkova
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  2. V. V. Shurygin
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Corresponding authors

Correspondence to S. K. Zubkova or V. V. Shurygin.

Additional information

Original Russian Text © S.K. Zubkova, V.V. Shurygin, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 5, pp. 80–85.

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Zubkova, S.K., Shurygin, V.V. Transverse Lie jets and holomorphic geometric objects on transverse bundles. Russ Math. 60, 70–74 (2016). https://doi.org/10.3103/S1066369X16050078

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  • DOI: https://doi.org/10.3103/S1066369X16050078

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