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RC-positive metrics on rationally connected manifolds

Xiaokui Yang

Complex Variables and Complex Analysis Differential Geometry Algebraic Geometry mathscidoc:2206.08002

Forum of Mathematics, Sigma, 8, e53, 1-19, 2020.11
In this paper, we prove that if a compact Kähler manifold X has a smooth Hermitian metric ω such that (T_X,ω) 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 .
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@inproceedings{xiaokui2020rc-positive,
  title={RC-positive metrics on rationally connected manifolds},
  author={Xiaokui Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220622155131973947451},
  booktitle={Forum of Mathematics, Sigma},
  volume={8},
  pages={e53, 1-19},
  year={2020},
}
Xiaokui Yang. RC-positive metrics on rationally connected manifolds. 2020. Vol. 8. In Forum of Mathematics, Sigma. pp.e53, 1-19. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220622155131973947451.
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