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The generalized Frankel conjecture in Sasaki geometry

Weiyong He SONG SUN

Differential Geometry mathscidoc:1912.43457

International Mathematics Research Notices, 2015, (1), 99-118, 2015
We prove some structure results for transversely reducible Sasaki manifolds. In particular, we show a Sasaki manifold with positive Ricci curvature is transversely irreducible, and so join (product) construction cannot be generalized to irregular SasakiEinstein manifolds, as opposed to the quasi-regular case done by WangZiller and BoyerGalicki. As an application, we classify compact Sasaki manifolds with nonnegative transverse bisectional curvature, which can be viewed as the generalized Frankel conjecture in Sasaki geometry.
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@inproceedings{weiyong2015the,
  title={The generalized Frankel conjecture in Sasaki geometry},
  author={Weiyong He, and SONG SUN},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114546386585017},
  booktitle={International Mathematics Research Notices},
  volume={2015},
  number={1},
  pages={99-118},
  year={2015},
}
Weiyong He, and SONG SUN. The generalized Frankel conjecture in Sasaki geometry. 2015. Vol. 2015. In International Mathematics Research Notices. pp.99-118. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114546386585017.
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