论文标题
复杂的表面和无编形杀死矢量场
Complex surfaces and null conformal Killing vector fields
论文作者
论文摘要
我们研究了伪造的伪造歧管上具有null保形杀死载体场的存在与兼容复合物和偏见的结构之间的关系（2,2）。我们首先建立了伪 - 温米特表面的拓扑类型，该表面无处可消失。然后，我们表明一对正交，线性独立的，无效的保形杀死矢量场定义了一个偏见的结构，并使用这一事实将其分类为平滑的紧凑型四个manifolds承认这样的矢量场。我们还提供了具有两个正交的，线性独立的，无效的杀死矢量场的中性指标的示例。
We study the relation between the existence of null conformal Killing vector fields and existence of compatible complex and para-hypercomplex structures on a pseudo-Riemannian manifold with metric of signature (2,2). We establish first the topological types of pseudo-Hermitian surfaces admitting a nowhere vanishing null vector field. Then we show that a pair of orthogonal, pointwise linearly independent, null, conformal Killing vector fields defines a para-hyperhermitian structure and use this fact for a classification of the smooth compact four-manifolds admitting such a pair of vector fields. We also provide examples of neutral metrics with two orthogonal, pointwise linearly independent, null Killing vector fields on most of these manifolds.
