A rigidity theorem for hypersurfaces with positive Möbius Ricci curvature

Abstract. Let M n (nミ3)be an immersed hypersurface without umbilic points in the (n + 1)-dimensional unit sphere sn+l. Then MII is associated with a so-called M凸biusfonn φand a Mobius metric 9 which are invariants of Mn under the Mobius transformation group of sn十1In this paper ， we show that ifφis identicaIly zero and the Ricci curvature Ricg is pinched: (n-l)(n-2)/12 ~ Ricg ~ (12-21 + 5)(1-2)/[12(1-1)] ， then it must be the case tl 凶 1 = 2p and Mn is Mめiusequivalent to SP(l/V2) x SP(l/v宝)