Let [M.sup.n] be an n-dimensional differentiable manifold endowed with a (1,1) tensor field [phi], a contravariant vector field [xi], a covariant vector
field [eta] and a Lorentzian metric g of type (0, 2) such that for each point p [member of] M, the tensor [g.sub.p]: [T.sub.p]M x [T.sub.p]M [right arrow] R is an inner product of signature (-, +, +, ..., +), where [T.sub.p]M denotes the tangent vector space of M at p and R is the real number space which satisfies
Starting from generic bilinear Hamiltonians, constructed by covariant vector, bivector or tensor fields, it is possible to derive a general symplectic structure which leads to holonomic and anholonomic formulations of Hamilton equations of motion directly related to a hydrodynamic picture.
We show that a covariant analogue of Hamilton equations can be derived from covariant vector (or tensor) fields in holonomic and anholonomic coordinates.
In fact, taking into account generic Hamiltonian invariants, constructed by covariant vectors, bivectors or tensors, it is possible to show that a symplectic structure can be achieved in any case.