A nef vector bundle on a projective variety is a vector bundle whose tautological quotient line bundle 
has nonnegative
degree on every curve. This uses the one-dimensional-quotient convention for the
projective bundle. A bundle generated by global
sections is nef, but nefness is weaker than ampleness.
On a compact complex manifold the analytic definition requires smooth Hermitian metrics on the tautological line
bundle with curvature bounded below by 
for every 
, for a fixed Hermitian
form 
on the projectivization. It agrees with numerical nefness in the projective setting.
The Campana-Peternell conjecture
concerns Fano manifolds with nef tangent
bundle.
