Bi-Hamiltonian structure of a unit geodesic vector field on a 3D space of constant negative curvature

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dc.authoridBayrakdar, Tuna/0000-0001-8777-5842
dc.authorwosidBayrakdar, Tuna/M-9387-2017
dc.contributor.authorBayrakdar, T.
dc.date.accessioned2024-06-12T10:55:58Z
dc.date.available2024-06-12T10:55:58Z
dc.date.issued2024
dc.departmentTrakya Üniversitesien_US
dc.description.abstractIn this work we consider the Riemannian manifold defined by the product of an integral curve of a Cauchy-Riemann vector field on the Poincare upper half -plane and its image in the tangent bundle. We show that for a Cauchy-Riemann vector field the Chern-Simons three -form identically vanishes and for the Killing vector field X = x theta x + y theta y the manifold is a space of constant negative curvature. We also show that the components of the connection 1 -form theta define compatible Poisson structures iff theta perpendicular to d theta is so(3)-valued. By virtue of this we obtain a bi-Hamiltonian structure of a unit geodesic vector field on the manifold. (c) 2024 Elsevier B.V. All rights reserved.en_US
dc.identifier.doi10.1016/j.geomphys.2024.105115
dc.identifier.issn0393-0440
dc.identifier.issn1879-1662
dc.identifier.scopus2-s2.0-85183492359en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://doi.org/10.1016/j.geomphys.2024.105115
dc.identifier.urihttps://hdl.handle.net/20.500.14551/19615
dc.identifier.volume198en_US
dc.identifier.wosWOS:001175453100001en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherElsevieren_US
dc.relation.ispartofJournal Of Geometry And Physicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectCauchy-Riemann Vector Fielden_US
dc.subjectSpace Of Constant Negative Curvatureen_US
dc.subjectBi-Hamiltonian Structureen_US
dc.subjectUnit Geodesic Vector Fielden_US
dc.subjectFormsen_US
dc.titleBi-Hamiltonian structure of a unit geodesic vector field on a 3D space of constant negative curvatureen_US
dc.typeArticleen_US

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