Classification of hypersurfaces with constant Mobius curvature in Sm+1

Let x : M-m -> Sm+1 be an m-dimensional umbilic-free hypersurface in an (m+1)-dimensional unit sphere Sm+1, with standard metric I = dx . dx. Let I I be the second fundamental form of isometric immersion x. Define the positive function rho = root m/m-1 parallel to I I - 1/mtr(I I)I parallel to. Then positive definite (0,2) tensor g = rho I-2 is invariant under conformal transformations of Sm+1 and is called Mobius metric. The curvature induced by the metric g is called Mobius curvature. The purpose of this paper is to classify the hypersurfaces with constant Mobius curvature.MathematicsSCI(E)0ARTICLE1-2193-21927