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SIGMA, 2017, Volume 13, 055, 17 pp.
(Mi sigma1255)
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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
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\paper Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds
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This publication is cited in the following articles:
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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
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