Griffiths positivity

Summary

Griffiths positivity is a notion of positive curvature for a holomorphic Hermitian vector bundle of any rank. It asks that the curvature of the Chern connection be positive when evaluated on one tangent vector and one fibre vector at a time. For line bundles it is the same as being a positive line bundle. Griffiths positive bundles are ample, and Griffiths asked whether the converse holds; this question is open in general.