东北数学（英文版）
東北數學（英文版）
동북수학（영문판）
NORTHEASTERN MATHEMATICAL JOURNAL
2007年
1期
15-23
,共9页
M(o)bius sectional curvature%M(o)bius form%M(o)bius second fundamental form%Blaschke tensor
Let x : M → Sn+1 be a hypersurface in the (n + 1)-dimensional unit sphere Sn+1 without umbilic point. The M(o)bius invariants of x under the M(o)bius transformation group of Sn+1 are M(o)bius metric, M(o)bius form, M(o)bius second fundamental form and Blaschke tensor. In this paper, we prove the following theorem: Let x: M → Sn+1 (n ≥ 2) be an umbilic free hypersurface in Sn+1with nonnegative M(o)bius sectional curvature and with vanishing M(o)bius form. Then x is locally M(o)bius equivalent to one of the following hypersurfaces: (i) the torus Sk(a) × Sn-k(√1-a2) with 1 ≤ k ≤ n - 1; (ii) the pre-image of the stereographic projection of the standard cylinder Sk × Rn-k (∩) Rn+1 with 1 ≤ k ≤ n - 1; (iii) the pre-image of the stereographic projection of the cone in Rn+1: ～x(u, v, t) = (tu, tv),where (u,v,t) ∈ Sk(a) × Sn-k-1( √1- a2) × R+.
