Meromorphic mappings on K\"ahler manifolds weakly sharing hyperplanes in Pⁿ (C)

In this paper, we study the uniqueness problem for linearly nondegenerate meromorphic mappings from a K\"ahler manifold into Pⁿ (C) satisfying a condition (C_) 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_) conditions for different non-negative numbers.