Dört boyuttaki poisson bi-vektörler

In this work, it is shown that a non-vanishing vector field on a four dimensional manifold is locally bi-Hamiltonian. We construct a method for computing the symplectic structures which make the given non-vanishing vector field Hamiltonian. The method uses solely the knowledge of the vector field but not its integral curves. Therefore the method proposes a way of constructing a bi-Hamiltonian structure for the dynamical system defined by the given vector field without requiring the solution of the dynamical system.