Let X be a projective manifold with numerically effective anticanonical bundle. By studying the Albanese map and the MRC fibration, we prove that its universal cover splits as \widetilde{X} =C^n \times Y \times Z, where Y is a projective manifold of trivial first Chern class and Z is rationally connected. It is a joint work with Andreas H?ring. If the time is permitted, we explain also its generalization to the klt pair case, a recent joint work with Shin-Ichi Matsumura.
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