Projective manifolds whose tangent bundles are numerically effective

Abstract

In 1979, Mori [Mo] proved the so-called Hartshorne-Frankel conjecture: Every projective n-dimensional manifold with ample tangent bundle is isomorphic to the complex projective space P,. A differential-geometric analogon assuming the existence of a K/ihler metric on X with positive holomorphic bisectional curvature is independently due to Siu-Yau [SY]. Thus it seems natural to classify projective manifolds X whose tangent bundle Tx satisfy a degenerate condition of ampleness: numerical effectivity (abbreviated by "nef'). This means that the tautological quotient line bundle d~(1) on F(Tx) is numerically effective, i.e. C_>_0