Mobius Homogeneous Hypersurfaces with One Simple Principal Curvature in S^n+1

Let Mob(S^n+1)denote the Mobius transformation group of S^n+1.A hypersurface f:N^n→S^n+1 is called a Mobius homogeneous hypersurface,if there exists a subgroup G■Mob^(S^n+1)such that the orbit G(p)={Ф(p)Ф∈G}=f(M^n).In this paper,we classify the Mobius homogeneous hypersurfaces in S^n+1 with at most one simple principal curvature up to a M?bius transformation.