Algebraic dependence and finiteness problems of differentiably nondegenerate meromorphic mappings on Kähler manifolds

Abstract

Abstract Let M be a complete Kähler manifold, whose universal covering is biholomorphic to a ball 𝔹 m (R 0) in ℂ m (0 < R 0 +∞). Our first aim in this paper is to study the algebraic dependence problem of differentiably meromorphic mappings. We will show that if k differentibility nonde-generate meromorphic mappings f 1, …, fk of M into ℙ n (ℂ) (n ≥ 2) satisfying the condition (Cρ ) and sharing few hyperplanes in subgeneral position regardless of multiplicity then f 1 Λ … Λ fk 0. For the second aim, we will show that there are at most two different differentiably nondegenerate meromorphic mappings of M into ℙ n (ℂ) sharing q (q ∼ 2N − n + 3 + O(ρ)) hyperplanes in N−subgeneral position regardless of multiplicity. Our results generalize previous finiteness and uniqueness theorems for differentiably meromorphic mappings of ℂ m into ℙ n (ℂ) and extend some previous results for the case of mappings on Kähler manifold.