We desribe the minimal configurations of the bosonic membrane potential, when the membrane wraps up in an irreducible way over $S^{ 1}\times S^{ 1}$. The membrane 2-dimensional spatial world volume is taken as a Riemann Surface of genus $g$ with an arbitrary metric over it. All the minimal solutions are obtained and described in terms of 1-forms over an associated U(1) fiber bundle, extending previous results. It is shown that there are no infinite dimensional valleys at the minima.
Categories: hep-th