论文标题
与Segre四分之一相关的Einstein-Weyl空间
The Einstein-Weyl spaces associated to Segre quartic surfaces
论文作者
论文摘要
我们发现，一个属属的紧凑型缩影空间的明确例子，其爱因斯坦 - 韦尔空间具有与DE安慰剂空间相差的连接成分。它在其上引起的爱因斯坦 - 韦尔结构是洛伦兹，真实分析，其间距类的大地测量都封闭而简单。爱因斯坦 - 韦尔结构的自动形态组的身份成分是圆，因此该结构对标准的DE Sitter结构不是同构。我们表明，随着Segre表面变形并收敛到标准的DE Sitter结构，这些Einstein-Weyl结构变形。 我们研究的MinitWistor空间是所谓的Segre四分之一表面。他们有一对真正的节点，在证明上述结果中起着至关重要的作用。这些奇异性还使我们能够构建不承认任何紧凑型的非紧凑型复杂表面的明确例子。
We find explicit examples of compact minitwistor spaces of genus one, whose Einstein-Weyl spaces have a connected component that is diffeomorphic to the de Sitter space. The induced Einstein-Weyl structure on it is Lorenzian, real-analytic, whose spacelike geodesics are all closed and simple. The identity component of the automorphism group of the Einstein-Weyl structure is the circle and therefore the structure is not isomorphic to the standard de Sitter structure. We show that these Einstein-Weyl structures deform as the Segre surfaces deform and converge to the standard de Sitter structure. The minitwistor spaces we study are the so-called Segre quartic surfaces. They have a real pair of nodes, which play a crucial role in proving the above results. These singularities also allow us to construct explicit examples of non-compact complex surfaces that do not admit any compactification.
