A note on Euler number of locally conformally K\"{a}hler manifolds

Teng Huang

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arXiv · 1908.02173

A note on Euler number of locally conformally K\"{a}hler manifolds

Teng Huang

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Abstract

Let $M^{2n}$ be a compact Riemannian manifold of non-positive (resp. negative) sectional curvature. We call $(M,J,\theta)$ a $d$(bounded) locally conformally K\"{a}hler manifold if the lifted Lee form $\tilde{\theta}$ on the universal covering space of $M$ is $d$(bounded). We shown that if $M^{2n}$ is homeomorphic to a $d$(bounded) LCK manifold, then its Euler number satisfies the inequality $(-1)^{n}\chi(M^{2n})\geq$ (resp. $>$) $0$.

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Teng Huang. 2019-07-10. A note on Euler number of locally conformally K\"{a}hler manifolds. https://arxiv.org/abs/1908.02173

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