Let Mn be an n\(n \geq 3)-dimensional complete connected and oriented hypersurface in Mn+1(c)(c \geq 0) with constant mean curvature H and with two distinct principal curvatures, one of which is simple. We show that (1) if c=1 and the squared norm of the second fundamental form of Mn satisfies a rigidity condition (1.3), then Mn is isometric to the Riemannian product S1(\sqrt{1-a2}) \times Sn-1(a); (2) if c=0, H \neq 0 and the squared norm of the second fundamental form of Mn satisfies S \geq n2H2/(n-1), then Mn is isometric to the Riemannian product Sn-1(a)\times R or S1(a) \times Rn-1

Let Mn be an n\(n \geq 3)-dimensional complete connected and oriented hypersurface in Mn+1(c)(c \geq 0) with constant mean curvature H and with two distinct principal curvatures, one of which is simple. We show that (1) if c=1 and the squared norm of the second fundamental form of Mn satisfies a rigidity condition (1.3), then Mn is isometric to the Riemannian product S1(\sqrt{1-a2}) \times Sn-1(a); (2) if c=0, H \neq 0 and the squared norm of the second fundamental form of Mn satisfies S \geq n2H2/(n-1), then Mn is isometric to the Riemannian product Sn-1(a)\times R or S1(a) \times Rn-1