Checkerboard incircular nets. Laguerre geometry and parametrisation
Abstract
We present a procedure which allows one to integrate explicitly the class of checkerboard IC-nets which has recently been introduced as a generalisation of incircular (IC) nets. The latter class of privileged congruences of lines in the plane is known to admit a great variety of geometric properties which are also present in the case of checkerboard IC-nets. The parametrisation obtained in this manner is reminiscent of that associated with elliptic billiards. Connections with discrete confocal coordinate systems and the fundamental QRT maps of integrable systems theory are made. The formalism developed in this paper is based on the existence of underlying pencils of conics and quadrics which is exploited in a Laguerre geometric setting.
Keywords
Cite
@article{arxiv.1808.07254,
title = {Checkerboard incircular nets. Laguerre geometry and parametrisation},
author = {Alexander I. Bobenko and Wolfgang K. Schief and Jan Techter},
journal= {arXiv preprint arXiv:1808.07254},
year = {2018}
}
Comments
33 pages, 16 figures