COVARIANT HYDRODYNAMICS OF FLUID MEMBRANES

We derive covariant, reparametrization invariant, hydrodynamical equations for a fluctuating fluid membrane, which describe both tangent-plane motion and shape-changing normal motion. We calculate the renormalization of parameters of a Rouse model in which there is a friction force proportional to the local membrane velocity. Our calculations include both the Fadeev-Popov determinant and a Liouville-like factor needed to ensure rotational invariance.