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, cilt.42, sa.5, ss.2452-2465, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 5
  • Basım Tarihi: 2018
  • Doi Numarası: 10.3906/mat-1708-33
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.2452-2465
  • Anahtar Kelimeler: Bi-Hamiltonian structure, Poisson structure, Cartan's method of equivalence, intransitive structure equations, Maurer-Cartan equations, ORDER LAGRANGIANS, INTEGRABILITY, SYSTEMS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.