Bi-Hamiltonian structure of a unit geodesic vector field on a 3D space of constant negative curvature
Küçük Resim Yok
Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In 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.
Açıklama
Anahtar Kelimeler
Cauchy-Riemann Vector Field, Space Of Constant Negative Curvature, Bi-Hamiltonian Structure, Unit Geodesic Vector Field, Forms
Kaynak
Journal Of Geometry And Physics
WoS Q Değeri
N/A
Scopus Q Değeri
Q2
Cilt
198
