Abstract

Let M be a complete Kähler manifold, whose universal covering is biholomorphic to a ball Bm(R0) in Cm (0<R0≤+∞). In this article, we will show that if three meromorphic mappings f1,f2,f3 of M into Pn(C) (n≥2) satisfying the condition (Cρ) and sharing q (q>2n+1+α+ρK) hyperplanes in general position regardless of multiplicity with certain positive constants K and α<1 (explicitly estimated), then f1=f2 or f2=f3 or f3=f1. Moreover, if the above three mappings share the hyperplanes with mutiplicity counted to level n + 1 then f1=f2=f3. Our results generalize the finiteness and uniqueness theorems for meromorphic mappings of Cm into Pn(C) sharing 2n + 2 hyperplanes in general position with truncated multiplicity.