Classification of hypersurfaces with parallel Mbius second fundamental form in S~(n+1)

Let M~n(n≥2) be an immersed umbilic-free hypersurface in the (n+1)-dimensional unit sphere S~(n+1). Then M~n is associated with a so-called Mobius metric g,and a Mobius second fundamental form B which are invariants of M~n under the Mobiustransformation group of S~(n+1). In this paper, we classify all umbilic-free hypersurfaces withparallel Mobius second fundamental form.