| Manifolds covered by lines are among the most studied objects of classical projective geometry. Fano manifolds of high index (hence with Picard group Z) give typical examples. One expects any manifold covered by lines to be a Fano fibration and this turns out to be true when the family of lines through the general point is large enough. The first principle referred to in the title says that good properties of our given manifold are inherited by the general fibre of the Fano fibration (when it exists). The second principle is more subtle and concerns the properties inherited by the variety of lines through a general point. Applications include classification results for secant or dual defective manifolds, manifolds of small degree, manifolds covered by large linear spaces or hyperquadrics, etc. |