  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.
