arXiv 1802.018642018-02-06math.CVmath.GR

用三元组圆共形参数化LoxoEm

Conformal Parametrisation of Loxodromes by Triples of Circles

Vladimir V. Kisil, James Reid

备注：: 14 pages. 9 PDF in four figures, AMS-LaTex
发表信息：: In: Bernstein S. (eds) Topics in Clifford Analysis. pp 313-330, 2019, Birkhäuser, Cham
DOI：: 10.1007/978-3-030-23854-4_15

摘要：

我们提供了一个参数化的斜驶线由三个特别安排的周期。该参数化在复平面的分式线性变换下是协变的，并且自然地编码了loxoplane的共形性质。选定的几何例子说明参数化的使用。我们的工作扩展了李球几何中的对象集-圆、线和点-到自然的最大共形不变族，其中也包括loxoetry。

英文摘要：

We provide a parametrisation of a loxodrome by three specially arranged cycles. The parametrisation is covariant under fractional linear transformations of the complex plane and naturally encodes conformal properties of loxodromes. Selected geometrical examples illustrate the usage of parametrisation. Our work extends the set of objects in Lie sphere geometry---circle, lines and points---to the natural maximal conformally-invariant family, which also includes loxodromes.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。