Moebius Equivalency Of Two Hypersurfaces In The Unit Sphere

Let x:M→Sn+1 be an immersed umbilic-free hupersurface in the (n+1)-dimensional unite sphere.According to Wang Changping's Mobius geometric theory of submanifolds, M is associated with a Mobius metric g, Mobius formΦ, Blaschke tensor A, Mobius second fundamental form B which are invariants of M under the Mobius transformation group of Sn+1. Based on the classification theorem for hypersurfaces having parallel Mobius sec-ond fundamental form presented by Hu Zejun and Li Haizhong and that for hypersurfaces having two distinct Blaschke eigenvalues presented by Li Xingxiao and Zhang Fengyun, we obtain the main theorem in this paper:Main Theorem:By the inverse of the stereographic projection change hypersur-face u:Sp(1/2^1/2)×Sp(1/2^1/2)×R+×Rn-2p-1→Rn+1 defined by u=(tu′,tu″,u(?)), where u′∈Sp(1/2^1/2),u″∈Sp(1/2^1/2),t∈R+,u(?)∈Rn-2p-1 to hypersurface in Sn+1 is locally Mobius equivalent to hypersurface Y:Sp((n-1)/pn)×Sp((n-1)/pn)×Hn-2p(-(n-1)/2pn)→Sn+1.