  Three-dimensional equi-potential surfaces of a galactic system with
supermassive binary black holes are discussed herein. The conditions of
topological transitions for the important surfaces, i.e. Roche Lobes and
Jiang-Yeh Lobe, are studied in this paper. In addition, the mathematical
properties of the Jacobi surfaces are investigated analytically. Finally, a
numerical procedure for determining the regions of the Roche Lobes and
Jiang-Yeh Lobe is suggested.
