Abstract

Let M be a complete Kähler manifold whose universal covering is biholomorphic to a ball in . In this paper, we will show that if two meromorphic mappings f and g from M into have the same inverse images for hyperplanes with multiplicities counted to level and satisfy the condition then the map is algebraically degenerate over , where is a positive integer and ρ is a non-negative number (explicitly estimated). Our result generalizes the previous result of H. Fujimoto for the case of mappings on to the case of mappings on a complete Kähler manifold as above M and also improves his result by giving an explicit estimate for the number .