双曲空间H^(n+p)(-1)中具有平行平均曲率的子流形

Submanifolds in Hyperbolic H~ n+p (-1) with Parallel Mean Curvature

设M n 是H n + p(- 1)中的具有平行平均曲率的完备子流形 ,当H2 ≥ 4 (n - 1) /n2 及第二基本形式S满足S≤nH2 +12 (n - 1) n3 (n - 1)H2 - 4n(n - 1) 2 - n(n - 2 )2n(n - 1)H2时 ,给出完备子流形M n 的一个分类 .

Let M n be a complete submanifold in H n+p (-1) with parallel mean curvature.If the second fundamental form S satifies S≤nH 2+JB<2*[SX(*812(n-1)SX)KF(n 3(n-1)H 2-4n(n-1) 2KF)-SX(*8n(n-2)2KF(n(n-1)KF)SX)HJB>2*] 2 ,we can classify the complete submanifold M n completely.