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Compact Kähler manifolds homotopic to negatively curved Riemannian manifolds

Bing-Long Chen Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China Xiaokui Yang Morningside Center of Mathematics, Institute of Mathematics, Hua Loo-Keng Key Laboratory of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Differential Geometry mathscidoc:2207.10003

Mathematische Annalen, 370, 1477–1489, 2017.2
In this paper, we show that any compact Kähler manifold homotopic to a compact Riemannian manifold with negative sectional curvature admits a Kähler–Einstein metric of general type. Moreover, we prove that, on a compact symplectic manifold X homotopic to a compact Riemannian manifold with negative sectional curvature, for any almost complex structure J compatible with the symplectic form, there is no non-constant J-holomorphic entire curve f:C→X.
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@inproceedings{bing-long2017compact,
  title={Compact Kähler manifolds homotopic to negatively curved Riemannian manifolds},
  author={Bing-Long Chen, and Xiaokui Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220703154100402621527},
  booktitle={Mathematische Annalen},
  volume={370},
  pages={1477–1489},
  year={2017},
}
Bing-Long Chen, and Xiaokui Yang. Compact Kähler manifolds homotopic to negatively curved Riemannian manifolds. 2017. Vol. 370. In Mathematische Annalen. pp.1477–1489. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220703154100402621527.
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