Let X be a complex smooth projective variety of dimension n, and let E be an ample vector bundle on X. In this paper, we will introduce new invariants of generalized polarized manifolds (X,E), and we will study their properties. As an application, we study a lower bound for c<sub>1</sub>(E)<sup>n</sup> and the sectional genus g(X, c<sub>1</sub>(E)) of (X, c<sub>1</sub>(E)).