Conformal geometry of flows in n dimensions
Conformal geometry of flows in n dimensions
复制标题
n 维流动的共形几何
DOI：
10.1063/1.525878
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发表时间：
1983
影响因子：
1.3
通讯作者：
A. Trautman
中科院分区：
文献类型：
--
作者：
I. Robinson;A. Trautman
从共形几何的角度考虑由平滑矢量场生成的流。如果流保持与流线正交的向量空间分布，则流被定义为共形测地线。此外，如果它保留了这些向量空间上的共形结构，那么它就是无剪切的。针对任意签名的 n 维共角空间的一般情况，导出了表征此类流的微分方程。在时空中零流的特殊情况下，我们获得了将麦克斯韦方程组的零解与测地线和无剪切的零流连接起来的定理的精炼版本。
Flows generated by smooth vector fields are considered from the point of view of conformal geometry. A flow is defined to be conformally geodesic if it preserves the distribution of vector spaces orthogonal to the lines of the flow. It is shear‐free if, moreover, it preserves the conformal structure on these vector spaces. Differential equations characterizing such flows are derived for the general case of an n‐dimensional conformal space of arbitrary signature. In the special case of null flows in spacetime, one obtains a refined version of the theorem connecting null solutions of Maxwell’s equations with null flows that are geodesic and shear‐free.