Transversity of a massless relativistic membrane

We consider the relativistic theory of the open two-dimensional surface, which is characterized by an action proportional to the volume sweptout by the surface in space time. It is shown that classically there are only D-3 dynamically independent transverse components among the D functions Xμ(σ1, σ2, τ) which represent the world volume (D is the dimension of space time) and that the surface boundary moves with velocity of light