- Turkish Journal of Mathematics
- Vol: 42 Issue: 5
- Equivalence problem for compatible bi-Hamiltonian structures on three-dimensional orientable manifol...
Equivalence problem for compatible bi-Hamiltonian structures on three-dimensional orientable manifolds
Authors : Tuna Bayrakdar, Abdullah Aziz Ergin
Pages : 2452-2465
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Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : Bi-Hamiltonian structure, Poisson structure, Cartan's method of equivalence, intransitive structure equations, Maurer--Cartan equations