  The three-dimensional Gross-Neveu model in $R^{1} \times S^{2}$ spacetime is
considered at finite particles number density. We evaluate an effective
potential of the composite scalar field $\sigma(x)$, which is expressed in
terms of a scalar curvature $R$ and nonzero chemical potential $\mu$. We then
derive the critical values of $(R,\mu)$ at which the system undergoes the first
order phase transition from the phase with broken chiral invariance to the
symmetric phase.
