Non-Euclidean Laguerre Geometry and Incircular Nets

Alexander Bobenko is a professor at the Technische Universität Berlin. He is an author with Yuri Suris of the book „Discrete Differential Geometry“, and editor of several books in geometry and mathematical physics. He is the Coordinator of the DFG Collaboration Research Center „Discretization in Geometry and Dynamics“.Carl Lutz is a doctoral student at Technische Universität Berlin. He wrote his master thesis under the supervision of Alexander Bobenko on the topic “Laguerre Geometry in Space Forms”.Helmut Pottmann is a professor at King Abdullah University of Science and Technology in Saudi Arabia and at Technische Universität Wien. He has co-authored two books (“Computational Line Geometry” and “Architectural Geometry”) and has been founding director of the Visual Computing Center at KAUST and the Center for Geometry and Computational Design at TU Wien.Jan Techter is a postdoc at Technische Universität Berlin. He wrote his doctoral thesis under the supervision of Alexander Bobenko on the topic “Discrete Confocal Quadrics and Checkerboard Incircular Nets”.

“In this short book the authors present non-Euclidean Laguerre geometry, related Möbius and Lie geometries, and their transformations, and demonstrate how these geometries can be applied to the study of checkerboard incircular nets. ... Two appendices summarize defnitions and properties of Euclidean Laguerre geometry and generalized signed inversive distance. Throughout the text, many instructive diagrams aid the visualization of the concepts and constructions.” (Günter F. Steinke, Mathematical Reviews, Issue 2, March, 2024)“The book is very geometric in flavour and contains lots of instructive illustrations.” (Norbert Knarr, zbMATH 1492.51001, 2022)

• Introduction.- Two-dimensional non-Euclidean Laguerre geometry.- Quadrics in projective space.- Cayley-Klein spaces.- Central projection of quadrics and Möbius geometry.- Non-Euclidean Laguerre geometry.- Lie geometry.- Checkerboard incircular nets.- Euclidean cases.- Generalized signed inversive distance.