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Symmetry, Integrability and Geometry: Methods and Applications, 2017, Volume 13, 055, 17 pp.
DOI: https://doi.org/10.3842/SIGMA.2017.055
(Mi sigma1255)
 

This article is cited in 2 scientific papers (total in 2 papers)

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
Full-text PDF (358 kB) Citations (2)
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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.
Received: December 21, 2016; in final form July 4, 2017; Published online July 14, 2017
Bibliographic databases:
Document Type: Article
MSC: 53D17; 53D35
Language: English
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 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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