  For the curved n-body problem, we show that the set of ordinary central
configurations is away from most singular configurations in H^3, and away from
a subset of singular configurations in S^3. We also show that each of the n!/2
geodesic ordinary central configurations for n masses has Morse index n-2. Then
we get a direct corollary that there are at least (3n-4)(n-1)!/2 ordinary
central configurations for given n masses if all ordinary central
configurations of these masses are non-degenerate.
