Bochner-Kaehler子流形的余维数

THE CODIMENSION OF BOCHNER-KAEHLER SUBMANIFOLD

设 M^n(n≥4)是复 n 维浸入在复 n+p 维 Bochner-Kaehler 流形■^(n+p)的完备 Bochner-Kaehler子流形时,H 是 M^n 在任意点 C∈M^n 的全纯截面曲率,■表示■^(n+p)在同点的全纯截面曲率的下确界.若 H<■,则 M^n 的余维数 p 不小于 n(n+1)/2.证明了在上述特殊情形下,Ogiue 猜想是正确的.

When M^n(n≥4)be a complete Bochner-Kaehler submanifold of complex dimension n,immersed in the Bochner-Kaehler manifold ^(n+p) of complex dimension n+p.Let H be the holomorphic sectional curvature of M^n,at any point C∈M^n and be the infimum of the holomorphic sectional curva- ture of ^(n+p) at same point.If H<,then the codimesion P of M^n is not less than (n(n+1))/2.Namely in the upper special case,the conjecture of Ogiue is correct.