论文标题
全面的Kähler歧管映射的变性定理，在投影空间中共享超平面
Degeneracy theorems for meromorphic mappings of a complete Kähler manifold sharing hyperplanes in a projective space
论文作者
论文摘要
让$ m $成为一个完整的kähler歧管，其通用覆盖物是$ \ mathbb b^m（r_0）$ in $ \ mathbb c^m $（$ 0 <r_0 \ le +\ le +\ infty $）。 In this article, we will show that if three meromorphic mappings $f^1,f^2,f^3$ of $M$ into $\mathbb P^n(\mathbb C)\ (n\ge 2)$ satisfying the condition $(C_ρ)$ and sharing $q\ (q> C+ρK)$ hyperplanes in general position regardless of multiplicity with certain positive constants $K$ and $C <2n $（明确估计），然后它们之间存在一些代数关系。还给出了$ k \（2 \ le k \ le n+1）$ meromormormormorphic映射共享超平面的变性定理。我们的结果将从$ \ mathbb c^m $映射到$ \ mathbb p^n（\ mathbb c）$的情况下概括了先前的结果。
Let $M$ be a complete Kähler manifold, whose universal covering is biholomorphic to a ball $\mathbb B^m(R_0)$ in $\mathbb C^m$ ($0<R_0\le +\infty$). In this article, we will show that if three meromorphic mappings $f^1,f^2,f^3$ of $M$ into $\mathbb P^n(\mathbb C)\ (n\ge 2)$ satisfying the condition $(C_ρ)$ and sharing $q\ (q> C+ρK)$ hyperplanes in general position regardless of multiplicity with certain positive constants $K$ and $C <2n$ (explicitly estimated), then there are some algebraic relation between them. A degeneracy theorem for $k\ (2\le k\le n+1)$ meromorphic mappings sharing hyperplanes is also given. Our result generalize the previous result in the case where the mappings from $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$.
