Article contents
RC-positive metrics on rationally connected manifolds
Published online by Cambridge University Press: 16 November 2020
Abstract
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
$T_X$
.
MSC classification
- Type
- Algebraic and Complex Geometry
- Information
- Creative Commons
- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Copyright
- © The Author(s), 2020. Published by Cambridge University Press
References
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20201116060208391-0839:S2050509420000328:S2050509420000328_inline4.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20201116060208391-0839:S2050509420000328:S2050509420000328_inline5.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20201116060208391-0839:S2050509420000328:S2050509420000328_inline6.png?pub-status=live)
- 4
- Cited by