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arXiv · 1809.01105

RC-positivity and scalar-flat metrics on ruled manifolds

Jun Wang·Xiaokui Yang
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Abstract

Let $X$ be a ruled surface over a curve of genus $g$. We prove that $X$ has a scalar-flat Hermitian metric if and only if $g\geq 2$ and $m(X)>2-2g$ where $m(X)$ is an intrinsic number depends on the complex structure of $X$.

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Jun Wang, Xiaokui Yang. 2018-09-04. RC-positivity and scalar-flat metrics on ruled manifolds. https://arxiv.org/abs/1809.01105

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