Geodesic
RC-positive metrics on rationally connected manifolds
Forum of Mathematics, Sigma, Tome 8 (2020)

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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 $T_X$. 
@article{10_1017_fms_2020_32,
     author = {Xiaokui Yang},
     title = {RC-positive metrics on rationally connected manifolds},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {8},
     year = {2020},
     doi = {10.1017/fms.2020.32},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2020.32/}
}
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Xiaokui Yang. RC-positive metrics on rationally connected manifolds. Forum of Mathematics, Sigma, Tome 8 (2020). doi: 10.1017/fms.2020.32

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