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Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 5, Pages 80–85 (Mi ivm9115)  

Brief communications

Transversal Lie jets and holomorphic geometric objects on transverse bundles

S. K. Zubkova, V. V. Shurygin

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

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.

Keywords: Weil algebra, geometric object, Lie jet, Weil bundle, transverse bundle.

Full text: PDF file (197 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:5, 70–74

Bibliographic databases:

UDC: 514.76
Received: 15.12.2015

Citation: S. K. Zubkova, V. V. Shurygin, “Transversal Lie jets and holomorphic geometric objects on transverse bundles”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 5, 80–85; Russian Math. (Iz. VUZ), 60:5 (2016), 70–74

Citation in format AMSBIB
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\by S.~K.~Zubkova, V.~V.~Shurygin
\paper Transversal Lie jets and holomorphic geometric objects on transverse bundles
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2016
\issue 5
\pages 80--85
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\jour Russian Math. (Iz. VUZ)
\yr 2016
\vol 60
\issue 5
\pages 70--74
\crossref{https://doi.org/10.3103/S1066369X16050078}
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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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