论文标题
Cahen-Wallach空间的保形转换
Conformal transformations of Cahen-Wallach spaces
论文作者
论文摘要
我们研究非恒定截面曲率（所谓的Cahen-Wallach空间）的不可分解的Lorentzian对称空间的共形转换。当Cahen-Wallach空间被合并弯曲时，其形成性转换是同性恋。使用此情况，我们表明，仅当它具有固定点时，同形弯曲的Cahen-Wallach空间的共形转换至关重要。然后，我们探讨了在形式弯曲的Cahen-Wallach空间上与紧凑型轨道空间作用的一组连形变换的可能性。我们表明，任何这样的群体都不能集中基本的同胸，对于Cahen-Wallach空间，假想类型的空间必须包含在异构体中。
We study conformal transformations of indecomposable Lorentzian symmetric spaces of non-constant sectional curvature, the so-called Cahen-Wallach spaces. When a Cahen-Wallach space is conformally curved, its conformal transformations are homotheties. Using this we show that a conformal transformation of a conformally curved Cahen-Wallach space is essential if and only if it has a fixed point. Then we explore the possibility of properly discontinuous groups of conformal transformations acting with a compact orbit space on a conformally curved Cahen-Wallach space. We show that any such group cannot centralise an essential homothety and that for Cahen-Wallach spaces of imaginary type must be contained within the isometries.
