In the second part, we investigate the compact submanifolds m with the parallel isoperimetric section in the real space forms rm ( c ) and prove that if there exists a parallel isoperimetric section on m, and the sectional curvature of m is always greater than zero, then m is contained in a hyper-sphere; and get that the gauss curvature of the compact surfaces m with constant mean curvature in constant curvature space r4 ( c ) is always greater than zero, then m is a totally geodesic surface or a sphere, where an isoperimetric on m means a unit normal vector field defined globally on m with m1 ( ) = constant (2)研究了實空間形式r~m(c)中具有平行等參截面的緊致子流形m,證明了具有一平行等參截面的子流形m,如果m的截面曲率恒正,則m包含在r~m(c)的一個超球面內(nèi);對于常曲率空間及r~4(c)中具有常平均曲率的緊致曲面m,如果m的高斯曲率處處大于零,則m或為r~m(c)中的全測地曲面或為一球面。這里m上的等參截面是m上整體定義的單位法向量場,使得m關(guān)于它的平均曲率m_1()是常數(shù)。