Differentiably nondegenerate Meromorphic mappings on K\"{a}hler manifolds weakly sharing hyperplanes

Abstract

In this paper, we study the uniqueness problem for differentiably nondegenerate meromorphic mappings from a K\"{a}hler manifold into $\P^n(\C)$ satisfying a condition $(C_\rho)$ and sharing hyperplanes in general position, where the condition that two meromorphic mappings $f,g$ have the same inverse image for some hyperplanes $H$ is replaced by a weaker one that $f^{-1}(H)\subset g^{-1}(H)$. An improvement on the algebraic dependence problem of differentiably nondegenerate meromorphic mappings also is given. Moreover, in this case, the condition $f^{-1}(H)\subset g^{-1}(H)$ is even omitted for some hyperplanes.