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Abstract In this paper, we prove that if a compact Kähler manifold X has a smooth Hermitian metric such that (TX, ) is uniformly RC-positive, then X is projective and rationally connected. Conversely, we show that, if a projective manifold X is rationally connected, then there exists a uniformly RC-positive complex Finsler metric on TX.
Xiaokui Yang (Wed,) studied this question.