Hartogs延拓定理的推广

An Extension of the Hartogs Theorem

主要证明以下定理:设(M,h)是一完备的Hermite流形D2α,l=B2l\B2α(α<1),其中B2α表示c2中以原点为圆心,α为半径的球.f∶D2α,l→M为任一全纯映射,令u=Trace(f dS2M),其中f 表示TM上的拉回映射,dS2M表示M上的度量.若H≤2｜ u｜2u3,则M满足Hartogs现象.(其中H表示M上的全纯截曲率, u表示u的协变微分.)

Let(M,h) be a complete Hermite manifold,D2a,1=B21\B2a(a<1),where denoted by B2a the ball of radius centered at the origin in C2. Suppose f is a holomorphic map from D2a,1into M, denote by u the trace of the (1,1)form f*dS2M,here f* is the pull back of f on TM, dS2M is the Hermite metric. If H≤2|u|2u3,then M obeys the Hartogs phenomenon..(here H is the holomorphic sectional curvature of M,u is the covariant derivative.)