Rational Homogeneous Variety

A rational homogeneous variety is a projective homogeneous space , where is a connected semisimple complex algebraic group and is a parabolic subgroup. The transitive action generates its tangent bundle by global sections, so that bundle is nef. Projective spaces and Grassmannians are examples.

The Campana-Peternell conjecture predicts that smooth complex Fano manifolds with nef tangent bundle all have this form.