Gradient vector fields on cosymplectic manifolds

The authors study some geometrical properties of gradient vector fields on cosymplectic manifolds, thereby emphasizing the close analogy with Hamiltonian systems on symplectic manifolds. It is shown that gradient vector fields and, more generally, local gradient vector fields can be characterized in terms of Lagrangian submanifolds of the tangent bundle with respect to an induced symplectic structure. In addition, the symmetry and reduction properties of gradient vector fields are investigated.