Willmore hypersurfaces with constant Mobius curvature in Rn+1

For an immersed hypersurface f : M-n -> Rn+1 without umbilical points, one can define the Mobius metric g on f which is invariant under the Mobius transformation group. The volume functional of g is a generalization of the well-known Willmore functional, whose critical points are called Willmore hypersurfaces. In this paper, we prove that if a n-dimensional Willmore hypersurfaces (n >= 3) has constant sectional curvature c with respect to g, then c = 0, n = 3, and this Willmore hypersurface is Mobius equivalent to the cone over the Clifford torus in S-3 subset of R-4. Moreover, we extend our previous classification of hypersurfaces with constant Mobius curvature of dimension n >= 4 to n = 3, showing that they are cones over the homogeneous torus S-1(r) x S-1(root 1 - r(2)) subset of S-3, or cylinders, cones, rotational hypersurfaces over certain spirals in the space form R-2, S-2, H-2, respectively.MathematicsSCI(E)0ARTICLE1251-26716