Conformal circles and parametrizations of curves in conformal manifolds
Conformal circles and parametrizations of curves in conformal manifolds
复制标题
共形流形中的共形圆和曲线参数化
DOI：
10.1090/s0002-9939-1990-0994771-7
复制
发表时间：
1990
期刊：
影响因子：
--
通讯作者：
M. Eastwood
中科院分区：
文献类型：
--
作者：
T. Bailey;M. Eastwood
我们给出了共形流形上的共形圆的简单常微分方程，它给出了曲线以及一系列首选参数化。这些参数化赋予每个共形圆一个投影结构。该方程分为两部分，其中一个给出独立于任何参数化的共形圆，另一个可以应用于任何曲线以显式生成它从环境共形结构继承的投影结构[1]。我们简要讨论了使用共形圆来给出点附近的首选坐标和度量，并概述了在四维情况下与扭量理论的关系。
We give a simple ODE for the conformal circles on a conformal manifold, which gives the curves together with a family of preferred parametrizations. These parametrizations endow each conformal circle with a projective structure. The equation splits into two pieces, one of which gives the conformal circles independent of any parameterization, and another which can be applied to any curve to generate explicitly the projective structure which it inherits from the ambient conformal structure [1]. We discuss briefly the use of conformal circles to give preferred coordinates and metrics in the neighborhood of a point, and sketch the relationship with twistor theory in the case of dimension four.