Non-Euclidean Laguerre geometry and incircular nets
Metric Geometry
2020-09-03 v1 Algebraic Geometry
Abstract
Classical (Euclidean) Laguerre geometry studies oriented hyperplanes, oriented hyperspheres, and their oriented contact in Euclidean space. We describe how this can be generalized to arbitrary Cayley-Klein spaces, in particular hyperbolic and elliptic space, and study the corresponding groups of Laguerre transformations. We give an introduction to Lie geometry and describe how these Laguerre geometries can be obtained as subgeometries. As an application of two-dimensional Lie and Laguerre geometry we study the properties of incircular nets.
Cite
@article{arxiv.2009.00978,
title = {Non-Euclidean Laguerre geometry and incircular nets},
author = {Alexander I. Bobenko and Carl O. R. Lutz and Helmut Pottmann and Jan Techter},
journal= {arXiv preprint arXiv:2009.00978},
year = {2020}
}
Comments
97 pages, 44 figures