论文标题
伪有源子手机在Kahler 4-manifolds中
Pseudoconvex submanifolds in Kahler 4-manifolds
论文作者
论文摘要
在Kahler 4-manifolds上，不一定是紧凑或有限的拓扑类型，我们获得了基本的紧凑型嵌入式Levi-flat或Pseudoconvex Submanifold与环境歧管$ M^4 $的基本组之间的关系。当levi-flat submanifold $ v^3 $具有有限的基本组时，$π_1（m^4）= i_*π_1（v^3）$;当非分离pseudoconvex submanifold $ v^3 $具有有限的基本组时，则$π_1（m^4）= i_*π_1（v^3）\ rtimes \ rtimes \ mathbb {z} $。作为应用，如果Kahler歧管（是否紧凑）具有嵌入式的全体形态$ \ Mathbb {p}^1 $的积极自行解剖，则必须相交，它必须与所有其他全态$ p^1 $ p^1 $ p^1 $ p^1 $ p^1 $ p^1 $ p^1 $ p^$ m^4 $ $ m^4 $ a $^4 $ no nes and Alf Infeart和Alf Enef。如果Levi-flat Submanifold和一个嵌入式的Holomorphic $ \ Mathbb {p}^1 $的正相交都存在，则它们相交。 ALE Plus Alf末端的总数为零，或者不管存在哪些其他末端。我们提供示例，例如2端标量牌卡勒度量标准度量。
On Kahler 4-manifolds, not necessarily compact or of finite topological type, we obtain relationships between the fundamental group of compact embedded Levi-flat or pseudoconvex submanifold and the fundamental group of the ambient manifold $M^4$. When a Levi-flat submanifold $V^3$ has finite fundamental group then $π_1(M^4)=ι_*π_1(V^3)$; when a non-separating pseudoconvex submanifold $V^3$ has finite fundamental group, then $π_1(M^4)=ι_*π_1(V^3)\rtimes\mathbb{Z}$. As applications, if a Kahler manifold (compact or not) has an embedded holomorphic $\mathbb{P}^1$ of positive self-intersection, it must intersect all other holomorphic $P^1$ of non-negative self-intersection, the fundamental group of $M^4$ is trivial, and no ALE or ALF ends exist. If a Levi-flat submanifold and an embedded holomorphic $\mathbb{P}^1$ of positive self-intersection both exist, they intersect. The total number of ALE plus ALF ends is zero or one regardless of what other kinds of ends exist. We provide examples, such as a 2-ended scalar-flat Kahler metric conformal to the Taub-NUT.
