Abstract: In this paper, we prove a Second Main Theorem for holomorphic mappings in a disk whose image intersects some families of nonlinear hypersurfaces (totally geodesic hypersurfaces with respect to a meromorphic connection) in the complex projective space $\mathbb{P}^k$. This is a generalization of Cartan's Second Main Theorem. As a consequence, we establish a uniqueness theorem for holomorphic mappings which intersect $O(k^3)$ many totally geodesic hypersurfaces.

Key words: Second Main Theorem, meromorphic connection, totally geodesic hypersurfaces, uniqueness theorem