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arXiv · 1609.06918

Compact K$\"a$hler manifolds homotopic to negatively curved Riemannian manifolds

Bing-Long Chen·Xiaokui Yang
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Abstract

In this paper, we show that any compact K$\"a$hler manifold homotopic to a compact Riemannian manifold with negative sectional curvature admits a K$\"a$hler-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 $f:C \rightarrow X$.

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Bing-Long Chen, Xiaokui Yang. 2016-09-22. Compact K$\"a$hler manifolds homotopic to negatively curved Riemannian manifolds. https://arxiv.org/abs/1609.06918

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