AI 中文总结
本文受非交换Carrollian几何启发，提出Carrollian-Poisson丛概念，要求Carroll分布含于Poisson锚像中，给出Kerr视界等例，并证明可配备相容Vaisman联络以定义几何运动学。
AI 中文摘要
受非交换Carrollian几何的启发，我们引入了Carrollian-Poisson丛的概念，将其理解为具有相容Poisson结构的Carrollian流形。相容性表示为Carroll分布包含于Poisson锚映射的像中。我们探讨了这种相容性的几何后果，并给出了几个Carrollian-Poisson丛的简单例子，包括（外部）Kerr视界、BTZ视界和未来零无穷远。此外，我们证明了每个Carrollian-Poisson丛都可以配备一个Vaisman（反变）联络，该联络既是度量相容的又是时钟相容的，从而可以定义和研究几何运动学。
英文摘要
We introduce, motivated by noncommutative Carrollian geometry, the notion of a Carrollian--Poisson bundle understood as a Carrollian manifold with a compatible Poisson structure. Compatibility is expressed as the inclusion of the Carroll distribution in the image of the Poisson anchor. We explore the geometric consequences of this compatibility and present several simple examples of Carrollian--Poisson bundles, including the (outer) Kerr horizon, the BTZ horizon, and future null infinity. Furthermore, we establish that every Carrollian--Poisson bundle can be equipped with a Vaisman (contravariant) connection that is both metric-compatible and clock-compatible, and thus geometric kinematics can be defined and studied.
Comments20 pages; comments welcomed
