A Uniqueness Theorem for Holomorphic Mappings in the Disk Sharing Totally Geodesic Hypersurfaces

In this paper, we prove a Second Main Theorem for holomorphic mappings in disk whose image intersects some families of nonlinear hypersurfaces (totally geodesic with respect to meromorphic connection) the complex projective space ℙk. This is generalization Cartan’s Theorem. As consequence, establish uniqueness theorem which intersect O(k3) many totally hypersurfaces.