论文标题
爱因斯坦自d-manifolds中超微小表面的calabi-yau属性
The Calabi-Yau property of superminimal surfaces in self-dual Einstein four-manifolds
论文作者
论文摘要
在本文中，我们表明，如果$（x，g）$是一个面向四维的爱因斯坦流形，它是自偶或反自我双对偶，则在$ x $的$ x $中，享受calabi-yau的属性，这意味着，这种类型的riemann表面上的每种沉浸式表面都可以与rieemann表面的每种沉浸式表面完整地覆盖。该证明使用扭曲空间的理论和复杂的接触歧管中的holomorphic legendrian曲线的卡拉比YAU特性。
In this paper, we show that if $(X,g)$ is an oriented four dimensional Einstein manifold which is self-dual or anti-self-dual then superminimal surfaces in $X$ of appropriate spin enjoy the Calabi-Yau property, meaning that every immersed surface of this type from a bordered Riemann surface can be uniformly approximated by complete superminimal surfaces with Jordan boundaries. The proof uses the theory of twistor spaces and the Calabi-Yau property of holomorphic Legendrian curves in complex contact manifolds.
