ABSTRACT

Let M be a complete Kähler manifold, whose universal covering is biholomorphic to a ball ${\mathbb{B}}^m\left(R_0\right)$ in ${\mathbb{C}}^m$ ($0<R_0\le +\mathrm{\infty }$). In this article, we will show that if three meromorphic mappings $f^1,f^2,f^3$ of M into ${\mathbb{P}}^n\left(\mathbb{C}\right)(n\ge 2)$ satisfying the condition $\left(C_{\rho }\right)$ and sharing $q(q>2n+1+\alpha +\rho K)$ hyperplanes in general position regardless of multiplicity with certain positive constants K and $\alpha <1$ (explicitly estimated), then $f^1=f^2$ or $f^2=f^3$ or $f^3=f^1$. Moreover, if the above three mappings share the hyperplanes with mutiplicity counted to level n + 1 then $f^1=f^2=f^3.$ Our results generalize the finiteness and uniqueness theorems for meromorphic mappings of ${\mathbb{C}}^m$ into ${\mathbb{P}}^n\left(\mathbb{C}\right)$ sharing 2n + 2 hyperplanes in general position with truncated multiplicity.

摘要

设M是一个完整的 Kähler 流形，它的普遍覆盖是双全纯球${\mathbb{乙}}^{米}\left({\mathrm{电阻}}_0\right)$ 在 ${\mathbb{C}}^{米}$ ($0<{\mathrm{电阻}}_0\le +\mathrm{\infty }$）。在本文中，我们将展示如果三个亚纯映射$F^1,F^2,F^3$的M成${\mathbb{磷}}^n\left(\mathbb{C}\right)(n\ge 2)$ 满足条件 $\left(C_{\rho }\right)$ 和分享 $q(q>2n+1+\alpha +\rho 钾)$处于一般位置的超平面与具有某些正常数K和的多重性无关$\alpha <1$ （显式估计），然后 $F^1=F^2$ 或者 $F^2=F^3$ 或者 $F^3=F^1$. 此外，如果上述三个映射共享具有多重性的超平面，则计为n  + 1级，则$F^1=F^2=F^3.$ 我们的结果概括了亚纯映射的有限性和唯一性定理 ${\mathbb{C}}^{米}$ 进入 ${\mathbb{磷}}^n\left(\mathbb{C}\right)$ 在具有截断多重性的一般位置共享 2 n + 2 个超平面。