  The conventional method to determine the cosmic curvature is to measure the
total mass density $\Omega_{\rm tot}$. Unfortunately the observational
$\Omega_{\rm tot}$ is closely near the critical value 1. The computation of
this paper shows that $\Omega_{\rm tot}\approx 1$ is an inevitable result for
the young universe independent of the spatial topology. So the mass density is
not a good criterion to determine the cosmic curvature. In this paper, we
derive a new criterion based on the galactic distribution with respect to
redshift $z$, which only depends on the cosmological principle and geometry.
The different type of spatial topology will give different results, then the
case can be definitely determined.
