Meromorphic mappings on K\"{a}hler manifolds weakly sharing hyperplanes in Pⁿ( C)

In this paper, we study the uniqueness problem for linearly nondegenerate meromorphic mappings from a K\"{a}hler manifold into Pⁿ( C) satisfying a condition (C_ρ) 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)⊂ g⁻¹(H). Moreover, we also give some improvements on the uniqueness problem and algebraic dependence problem of meromorphic mappings which share hyperplanes and satisfy (C_ρ) conditions for different non-negative numbers ρ.