English

Conformal dual of a quadruplet of points

Geometric Topology 2016-03-21 v2

Abstract

Let {P1,P2,P3,P4}\{P_1, P_2, P_3, P_4\} be a quadruplet of points in S3S^3 . 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.

Keywords

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