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RC-positive metrics on rationally connected manifolds
Part of
Xiaokui Yang
Journal:

Forum of Mathematics, Sigma / Volume 8 / 2020

Published online by Cambridge University Press:

16 November 2020, e53
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In this paper, we prove that if a compact Kähler manifold X has a smooth Hermitian metric $\omega $ such that $(T_X,\omega )$ 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 $T_X$ .