  We investigate four-fermion interactions with $N$-component fermion in
Einstein universe for arbitrary space-time dimensions ($2 \leq D<4$). It is
found that the effective potential for composite operator $\overline{\psi}\psi$
is calculable in the leading order of the $1/N$ expansion. The resulting
effective potential is analyzed by varying the curvature of the space-time and
is found to exhibit the symmetry restoration through the second-order phase
transition. The critical curvature at which the dynamical fermion mass
disappears is analytically calculated.
