Equivalence problem for compatible bi-Hamiltonian structures on three-dimensional orientable manifolds

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Bayrakdar T., ERGİN A. A.

TURKISH JOURNAL OF MATHEMATICS, vol.42, no.5, pp.2452-2465, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 5
  • Publication Date: 2018
  • Doi Number: 10.3906/mat-1708-33
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.2452-2465
  • Keywords: Bi-Hamiltonian structure, Poisson structure, Cartan's method of equivalence, intransitive structure equations, Maurer-Cartan equations, ORDER LAGRANGIANS, INTEGRABILITY, SYSTEMS
  • Akdeniz University Affiliated: Yes

Abstract

We solve the equivalence problem for compatible bi-Hamiltonian structures on three-dimensional orientable manifolds via Cartan's method of equivalence. The problem separates into two branches on total space, one of which ends up with the intransitive involutive structure equations. For the transitive case, we obtain an {e}-structure on both total and base spaces.