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arXiv · 1409.2404

Rational curves on Hermitian manifolds

Huitao Feng·Kefeng Liu·Xueyuan Wan·Xiaokui Yang
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Abstract

By using analytic method, we prove that there exist rational curves on compact Hermitian manifolds with positive holomorphic bisectional curvature. It confirms a question of S.-T. Yau. It is well-known that Mori proved in \cite{Mori79} that every compact complex manifold $N$ with $c_1(N)>0$ contains at least one rational curve. However, as a borderline example, we show that the standard Hopf surface $S^1\times S^3$ has a Hermitian metric with non-negative holomorphic bisectional curvature (in particular, $c_1(S^1\times S^3)\geq 0$), but it contains no rational curve.

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BibTeXRIS

Huitao Feng, Kefeng Liu, Xueyuan Wan, Xiaokui Yang. 2014-09-08. Rational curves on Hermitian manifolds. https://arxiv.org/abs/1409.2404

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