Phase space action for minimal surfaces of any dimension in curved spacetime

The phase space action, depending on coordinates, momenta and Lagrange multipliers (which turn out to be components of the induced metric), has been written down for a world sheet of arbitrary dimension (a string generalized to membranes) in a curved embedding spacetime. Canonical and hamiltonian formalisms have been formulated in a covariant and general way with the true dynamical variables being separated from the redundant ones. The membrane constraints follow directly from the variation of our action; their suitable superposition gives a hamiltonian from which we derive the equations of motion for a membrane via the Poisson brackets. The same hamiltonian we obtain also in a different way from a variation of the action. For n=2 all equations coincide with those of strings. (orig.)