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Izv. Vyssh. Uchebn. Zaved. Mat., 2019, Number 2, Pages 82–88 (Mi ivm9442)  

This article is cited in 1 scientific paper (total in 1 paper)

Brief communications

Holonomy pseudogroup of a manifold over the algebra of dual numbers and some its applications

A. A. Malyugina, V. V. Shurygin

Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: We study properties of the holonomy pseudogroup on a total immersed transversal of the canonical foliation on a smooth manifold over the algebra of dual numbers $\mathbb{D}$. We apply holonomy pseudogroups to the investigation of $\mathbb{D}$-diffeomorphisms between quotient manifolds of the algebra $\mathbb{D}$ by lattices and between $\mathbb{D}$-smooth manifolds naturally associated with an affine manifold.

Keywords: affine manifold, manifold over the algebra of dual numbers, foliation, foliated bundle, tangent bundle, tangent manifold, torus over the algebra of dual numbers, Weil bundle.

DOI: https://doi.org/10.26907/0021-3446-2019-2-82-88

Full text: PDF file (189 kB)
References: PDF file   HTML file

UDC: 514.76
Received: 20.09.2018
Revised: 20.09.2018
Accepted: 26.09.2018

Citation: A. A. Malyugina, V. V. Shurygin, “Holonomy pseudogroup of a manifold over the algebra of dual numbers and some its applications”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 2, 82–88

Citation in format AMSBIB
\Bibitem{MalShu19}
\by A.~A.~Malyugina, V.~V.~Shurygin
\paper Holonomy pseudogroup of a manifold over the algebra of dual numbers and some its applications
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2019
\issue 2
\pages 82--88
\mathnet{http://mi.mathnet.ru/ivm9442}
\crossref{https://doi.org/10.26907/0021-3446-2019-2-82-88}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Malyugina, V. V. Shurygin, “Psevdogruppy golonomii kak prepyatstviya k ekvivalentnosti mnogoobrazii nad algebroi dualnykh chisel”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 161, no. 3, Izd-vo Kazanskogo un-ta, Kazan, 2019, 438–455  mathnet  crossref
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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