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SIGMA, 2017, Volume 13, 055, 17 pp. (Mi sigma1255)  

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

Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds

Melike Išim Efe, Ender Abadoğlu

Yeditepe University, Mathematics Department, İnȯnu Mah. Kayışdağı Cad. 326A, 26 Ağustos Yerleşimi, 34755 Ataşehir İstanbul, Turkey

Abstract: In this work, we show that an autonomous dynamical system defined by a nonvanishing vector field on an orientable three-dimensional manifold is globally bi-Hamiltonian if and only if the first Chern class of the normal bundle of the given vector field vanishes. Furthermore, the bi-Hamiltonian structure is globally compatible if and only if the Bott class of the complex codimension one foliation defined by the given vector field vanishes.

Keywords: bi-Hamiltonian systems; Chern class; Bott class.

DOI: https://doi.org/10.3842/SIGMA.2017.055

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Bibliographic databases:

MSC: 53D17; 53D35
Received: December 21, 2016; in final form July 4, 2017; Published online July 14, 2017
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Citation: Melike Išim Efe, Ender Abadoğlu, “Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds”, SIGMA, 13 (2017), 055, 17 pp.

Citation in format AMSBIB
\Bibitem{IsiAba17}
\by Melike~I{\v s}im Efe, Ender~Abado{\u g}lu
\paper Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds
\jour SIGMA
\yr 2017
\vol 13
\papernumber 055
\totalpages 17
\mathnet{http://mi.mathnet.ru/sigma1255}
\crossref{https://doi.org/10.3842/SIGMA.2017.055}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000405963600001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85026366221}


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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. T. Bayrakdar, A. A. Ergin, “Equivalence problem for compatible bi-Hamiltonian structures on three-dimensional orientable manifolds”, Turk. J. Math., 42:5 (2018), 2452–2465  crossref  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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