论文标题
关于时空结构的固有扭转
On the intrinsic torsion of spacetime structures
论文作者
论文摘要
我们简要回顾了$ g $结构的固有扭转概念，然后继续对与SpaceTimes相关的$ G $结构的内在扭转进行分类：即Galilean（或Newton-Cartan），Carrollian，Aristotelian和Bargmannian。就伽利略结构而言，内在的扭转分类与众所周知的分类分类为无扭转，无扭曲的扭转和扭转的牛顿 - 卡丹几何形状。对于Carrollian结构，我们发现固有的扭转使我们能够将Carroll歧管分为四个类，这取决于Carroll Vector Field在空间度量上的作用，或者根据lorentzian歧管的无效性曲面的性质，或等效地将其变成carrollian colorlian segrolian segrolian segrolian segrolian segrolian segrolian segrotry可能会嵌入。通过对加利利和卡洛利亚结构的结果的一小部分，我们表明有16种的亚里士多德结构，我们以几何形式表征它们。最后，大部分纸张专门针对Bargmannian结构，在那里我们发现了二十七个类，我们也以几何表征，同时将其中一些与Galilean和Carrollian结构联系起来。 本文献给了Dmitri Vladimirovich Alekseevsky 80岁生日。
We briefly review the notion of the intrinsic torsion of a $G$-structure and then go on to classify the intrinsic torsion of the $G$-structures associated with spacetimes: namely, galilean (or Newton-Cartan), carrollian, aristotelian and bargmannian. In the case of galilean structures, the intrinsic torsion classification agrees with the well-known classification into torsionless, twistless torsional and torsional Newton-Cartan geometries. In the case of carrollian structures, we find that intrinsic torsion allows us to classify Carroll manifolds into four classes, depending on the action of the Carroll vector field on the spatial metric, or equivalently in terms of the nature of the null hypersurfaces of a lorentzian manifold into which a carrollian geometry may embed. By a small refinement of the results for galilean and carrollian structures, we show that there are sixteen classes of aristotelian structures, which we characterise geometrically. Finally, the bulk of the paper is devoted to the case of bargmannian structures, where we find twenty-seven classes which we also characterise geometrically while simultaneously relating some of them to the galilean and carrollian structures. This paper is dedicated to Dmitri Vladimirovich Alekseevsky on his 80th birthday.
