Conformal dual of a quadruplet of points
Geometric Topology
2016-03-21 v2
Abstract
Let be a quadruplet of points in . We define a ``dual'' quadruplet of it in a conformal geometric way. We show that the dual of a dual quadruplet coincides with the original one. We also show that the cross ratio of the dual quadruplet is equal to the complex conjugate of that of the original one.
Cite
@article{arxiv.0709.0454,
title = {Conformal dual of a quadruplet of points},
author = {Jun O'Hara},
journal= {arXiv preprint arXiv:0709.0454},
year = {2016}
}
Comments
This is a second version. A very short section was added at the end, where a cocircular case, which is a special case, was studied. A result in elementary geometry, especially, inversive geometry. 9 pages, 9 figures