A note on the dziobek central configurations

© 2015 American Mathematical Society. For the Newtonian n-body problem in ℝn−2 with n ≥ 3 we prove that the following two statements are equivalent. (a) Let x be a Dziobek central configuration having one mass located at the center of mass. (b) Let x be a central configuration formed by n−1 equal masses located at the vertices of a regular (n−2)-simplex together with an arbitrary mass located at its barycenter.