FANO MANIFOLDS WITH NEF TANGENT BUNDLES ARE WEAKLY ALMOST KAHLER-EINSTEIN

摘要

The goal of this short note is to point out that every Fano manifold with a nef tangent bundle possesses an almost Kahler-Einstein metric, in a weak sense. The technique relies on a regularization theorem for closed positive (1, 1)-currents. We also discuss related semistability questions and Chern inequalities.