Skip to main content
SpringerLink
Log in

Non-Euclidean Laguerre Geometry and Incircular Nets

  • Book
  • © 2021

Overview

Authors:
  1. Alexander I. Bobenko

    1. Institut für Mathematik, Technische Universität Berlin, Berlin, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Carl O.R. Lutz

    1. Institut für Mathematik, Technische Universität Berlin, Berlin, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  3. Helmut Pottmann

    1. Visual Computing Center, KAUST, Thuwal, Saudi Arabia

    View author publications

    You can also search for this author in PubMed   Google Scholar

  4. Jan Techter

    1. Institut für Mathematik, Technische Universität Berlin, Berlin, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • The first systematic introduction to non-Euclidean Laguerre geometry in the literature
  • Demonstrates all features of Laguerre geometry in terms of one recent application: checkerboard incircular nets
  • Beautifully illustrated by many render images

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (8 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Introduction

    • Alexander I. Bobenko, Carl O. R. Lutz, Helmut Pottmann, Jan Techter
    Pages 1-4

  3. Two-Dimensional Laguerre Geometry

    • Alexander I. Bobenko, Carl O. R. Lutz, Helmut Pottmann, Jan Techter
    Pages 5-18

  4. Quadrics in Projective Space

    • Alexander I. Bobenko, Carl O. R. Lutz, Helmut Pottmann, Jan Techter
    Pages 19-25

  5. Cayley-Klein Spaces

    • Alexander I. Bobenko, Carl O. R. Lutz, Helmut Pottmann, Jan Techter
    Pages 27-36

  6. Central Projection of Quadrics and Möbius Geometry

    • Alexander I. Bobenko, Carl O. R. Lutz, Helmut Pottmann, Jan Techter
    Pages 37-56

  7. Non-Euclidean Laguerre Geometry

    • Alexander I. Bobenko, Carl O. R. Lutz, Helmut Pottmann, Jan Techter
    Pages 57-69

  8. Lie Geometry

    • Alexander I. Bobenko, Carl O. R. Lutz, Helmut Pottmann, Jan Techter
    Pages 71-80

  9. Checkerboard Incircular Nets

    • Alexander I. Bobenko, Carl O. R. Lutz, Helmut Pottmann, Jan Techter
    Pages 81-115

  10. Back Matter

    Pages 117-137
    Download chapter PDF
Back to top

Keywords

About this book

This textbook is a comprehensive and yet accessible introduction to non-Euclidean Laguerre geometry, for which there exists no previous systematic presentation in the literature. Moreover, we present new results by demonstrating all essential features of Laguerre geometry on the example of checkerboard incircular nets.


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 checkerboard incircular nets.





Reviews

“The book is very geometric in flavour and contains lots of instructive illustrations.” (Norbert Knarr, zbMATH 1492.51001, 2022)

Authors and Affiliations

  • Institut für Mathematik, Technische Universität Berlin, Berlin, Germany

    Alexander I. Bobenko, Carl O.R. Lutz, Jan Techter

  • Visual Computing Center, KAUST, Thuwal, Saudi Arabia

    Helmut Pottmann

About the authors

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”.


Bibliographic Information

  • Book Title: Non-Euclidean Laguerre Geometry and Incircular Nets

  • Authors: Alexander I. Bobenko, Carl O.R. Lutz, Helmut Pottmann, Jan Techter

  • Series Title: SpringerBriefs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-81847-0

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

  • Softcover ISBN: 978-3-030-81846-3Published: 30 October 2021

  • eBook ISBN: 978-3-030-81847-0Published: 29 October 2021

  • Series ISSN: 2191-8198

  • Series E-ISSN: 2191-8201

  • Edition Number: 1

  • Number of Pages: X, 137

  • Number of Illustrations: 4 b/w illustrations, 53 illustrations in colour

  • Topics: Geometry, Projective Geometry, Hyperbolic Geometry

Publish with us

Policies and ethics

Back to top

Search

Navigation