The Uniqueness And Existence Of Centroaffine Hypersurfaces

It is well-known that for any hypersurface immersion x : M → An+1 such that x is transversal to x (TM) there exists aG-invariant bilinear form g and cubic form A, x is called a centroaffine hypersurface if g is nondegenerate. In this paper, we will first introduce connection form g and cubic form A, then westudied centroaffine hypersurfaces in (n + 1) -dimensional affinespace An+1 and got the uniqueness and existence of centroaffinehypersurfaces.