论文标题
射影表面和伪塑形曲线的可分离性
Metrisability of projective surfaces and pseudo-holomorphic curves
论文作者
论文摘要
我们表明，定向的射影表面的可分胜性等效于伪塑形曲线的存在。一个投影结构$ \ mathfrak {p} $和一个方向的表面$ m $上的音量表格$σ$，配备了一对$（J _ {\ Mathfrak {p}}，\ Mathfrak {j} _ {j} _ {\ Mathfrak strupter of Mathfrak {p} $ construps of a Pair $ z \ to m $ to m $ $ m $上的共形结构对应于$ z \至m $的部分，$ \ m athfrak {p} $在$ g $ g $ i时，仅当$ [g]：m \ to z $是一个伪型旋转曲线，而不是$ j _ { $ \ mathfrak {j} _ {\ mathfrak {p}，da_g} $。
We show that the metrisability of an oriented projective surface is equivalent to the existence of pseudo-holomorphic curves. A projective structure $\mathfrak{p}$ and a volume form $σ$ on an oriented surface $M$ equip the total space of a certain disk bundle $Z\to M$ with a pair $(J_{\mathfrak{p}},\mathfrak{J}_{\mathfrak{p},σ})$ of almost complex structures. A conformal structure on $M$ corresponds to a section of $Z\to M$ and $\mathfrak{p}$ is metrisable by the metric $g$ if and only if $[g] : M \to Z$ is a pseudo-holomorphic curve with respect to $J_{\mathfrak{p}}$ and $\mathfrak{J}_{\mathfrak{p},dA_g}$.
