Title: Conformally homogeneous Lorentzian spaces Show Chinese title

Title: 共形齐次洛伦兹空间

Abstract: We prove that if a 1-connected non-conformally flat conformal Lorentzian manifold $(M,c)$ admits a connected essential transitive group of conformal transformations, then there exists a metric $g\in c$ such that $(M,g)$ is a complete homogeneous plane wave. This finishes the classification of 1-connected Lorentzian manifolds, which admit transitive essential conformal group. We also prove that the group of conformal transformations of a non-conformally flat 1-connected homogeneous plane wave $(M,g)$ consists of homotheties, and it is a 1-dimensional extension of the group of isometries. Show Chinese abstract

Abstract: 我们证明，如果一个1连通的非共形平坦的共形洛伦兹流形$(M,c)$允许一个连通的本质传递的共形变换群，则存在一个度量$g\in c$使得$(M,g)$是一个完整的齐次平面波。 这完成了对允许传递的本质共形群的1连通洛伦兹流形的分类。 我们还证明，一个非共形平坦的1连通齐次平面波$(M,g)$的共形变换群由相似变换组成，并且它是等距群的一个1维扩展。