Title: On Dziobek Special Central Configurations,
Abstract: We study the special central configurations of the curved N-body problem in
S^3. We show that there are special central configurations formed by N masses
for any N >2. We then extend the concept of special central configurations to
S^n, n>0, and study one interesting class of special central configurations in
S^n, the Dziobek special central configurations. We obtain a criterion for them
and reduce it to two sets of equations. Then we apply these equations to
special central configurations of 3 bodies on S^1, 4 bodies on S^2, and 5
bodies in S^3.