CONFORMAL INVARIANTS OF THE EXTRINSIC GEOMETRY OF RELATIVISTIC MEMBRANES

We examine the change induced in the worldsheet geometry of a relativistic membrane under a conformal rescaling of the spacetime metric. As the induced transformation of the intrinsic geometry is obvious, the extrinsic geometry can be transformed nontrivially. By identifying the worldsheet scalars which transform multiplicatively, we can construct actions for extended objects which are conformally invariant.