Membrane geometry with auxiliary variables and quadratic constraints

Consider a surface described by a Hamiltonian which depends only on the metric and extrinsic curvature induced on the surface. The metric and the curvature, along with the basis vectors which connect them to the embedding functions defining the surface, are introduced as auxiliary variables by adding appropriate constraints, all of them quadratic. The response of the Hamiltonian to a deformation in each of the variables is determined and the relationship between the multipliers implementing the constraints and the conserved stress tensor of the theory established. For the purpose of illustration, a fluid membrane described by a Hamiltonian quadratic in curvature is considered.