Compact Kahler manifolds homotopic to negatively curved Riemannian manifolds

杨晓奎 Morningside center of Mathematics, Institute of Mathematics, CAS 陈兵龙 Department of Mathematics, Sun Yat-sen University

Differential Geometry mathscidoc:1609.10343

Math. Ann.
In this paper, we show that any compact K\"ahler manifold homotopic to a compact Riemannian manifold with negative sectional curvature admits a K\"ahler-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 $f:\C\> X$.
Kahler-Einstein metric
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@inproceedings{杨晓奎compact,
  title={Compact Kahler manifolds homotopic to negatively curved Riemannian manifolds},
  author={杨晓奎, and 陈兵龙},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160923173055441081046},
  booktitle={Math. Ann.},
}
杨晓奎, and 陈兵龙. Compact Kahler manifolds homotopic to negatively curved Riemannian manifolds. In Math. Ann.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160923173055441081046.
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