On projective varieties with strictly nef tangent bundles.

In this paper, we study smooth complex projective varieties X such that some exterior power ⋀ r T X of the tangent bundle is strictly nef. We prove that such varieties are rationally connected. We also classify the following two cases. If T X is strictly nef, then X isomorphic to the projective space P n. If ⋀ 2 T X is strictly nef and if X has dimension at least 3, then X is either isomorphic to P n or a quadric Q n. [ABSTRACT FROM AUTHOR]