Degeneracy theorems for meromorphic mappings of complete Kahler manifolds sharing hyperplanes in projective spaces

Let M be a complete Ka spexpressioncing diexpressioneresis hler manifold, whose universal covering is biholomorphic to a ball B-m(R-0) in C-m (0 < R-0 < +infinity). In this article, we will show that if three meromorphic mappings f1, f2, f3 of M into P-n(C) (n >= 2) satisfy the condition (C-rho) and share q (q > C + rho K) hyperplanes in general position regardless of multiplicity with certain positive constants K and C < 2n (explicitly estimated), then there are some algebraic relations between them. A degeneracy theorem for the product of k (2 < k < n + 1) meromorphic mappings sharing hyperplanes is also given. Our results generalize the previous results in the case of meromorphic mappings from C-m into P-n(C).