Abstract
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.