Topologically, a class of isomorphism of a complex vector bundle E-->X (of rank n) is equivalent to a homotopy class of its classifying map X-->BG(GL_n). Then, What is the geometric meaning (if any) of the positivity in a vector bundle? n>1. Intuitively, can such a classifying map turn out to be an embedding for a specific type of bundle? as it is in the case of positive line bundles?