A non-integrated defect relation for holomorphic maps into algebraic varieties

In 1983, relating to the study of value distribution of the Guass maps of complete minimal surfaces in ${\mathbb{R}}^m$, H. Fujimoto introduced the notion of the non-integrated defect for holomorphic maps of an open Riemann surface into ${\mathbb{P}}^n(\mathbb{C})$ and obtained some results analogous to the Nevanlinna-Cartan defect relation. This paper establishes the non-integrated defect relation for holomorphic maps into projective varieties.