A generalization of curve genus for ample vector bundles, II

Let X be a compact complex manifold of dimension n greater than or equal to 2 and E an ample vector bundle of rank r < n on X. As the continuation of Part I, we further study the properties of g(X, E) that is an invariant for pairs (X; E) and is equal to curve genus when r = n - 1. Main results are the classifications of (X, E) with g(X, E) = 2 (resp. 3) when E has a regul ar section (resp. E is ample and spanned) and 1 < r < n - 1.