Checkerboard Incircular Nets

Alexander I. Bobenko*, Carl O.R. Lutz, Helmut Pottmann, Jan Techter

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


In this section, as an application of two-dimensional Lie and Laguerre geometry, we present new research results. While incircular nets and their Laguerre geometric generalization to checkerboard incircular nets have been studied in great detail [Böh1970, AB2018, BST2018], we introduce their generalization to Lie geometry, and show that they may be classified in terms of checkerboard incircular nets in hyperbolic/elliptic/Euclidean Laguerre geometry. We prove incidence theorems of Miquel type, show that all lines of a checkerboard incircular net are tangent to a hypercycle, and give explicit formulas in terms of Jacobi elliptic functions. This generalizes the results from [BST2018] and leads to a unified treatment of checkerboard incircular nets in all space forms.

Original languageEnglish (US)
Title of host publicationSpringerBriefs in Mathematics
PublisherSpringer Science and Business Media B.V.
Number of pages35
StatePublished - 2021

Publication series

NameSpringerBriefs in Mathematics
ISSN (Print)2191-8198
ISSN (Electronic)2191-8201

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

ASJC Scopus subject areas

  • General Mathematics


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