Abstract
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 language | English (US) |
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Title of host publication | SpringerBriefs in Mathematics |
Publisher | Springer Science and Business Media B.V. |
Pages | 81-115 |
Number of pages | 35 |
DOIs | |
State | Published - 2021 |
Publication series
Name | SpringerBriefs in Mathematics |
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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