Non-Euclidean Laguerre geometry and incircular nets / Alexander I. Bobenko, Carl O.R. Lutz, Helmut Pottmann, Jan Techter.
Bobenko, Alexander I., author.; Lutz, Carl O. R., author.; Pottmann, Helmut, author.; Techter, Jan, author.
2021
QA551 .B63 2021
Available Online

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Title Non-Euclidean Laguerre geometry and incircular nets / Alexander I. Bobenko, Carl O.R. Lutz, Helmut Pottmann, Jan Techter.
Author Bobenko, Alexander I., author.
ISBN 9783030818470 (electronic bk.)
3030818470 (electronic bk.)
9783030818463
3030818462
DOI https://doi.org/10.1007/978-3-030-81847-0
Published Cham : Springer, [2021]
Copyright ©2021
Language English
Description 1 online resource : illustrations (chiefly color)
Item Number 10.1007/978-3-030-81847-0 doi
Call Number QA551 .B63 2021
Dewey Decimal Classification 516.3
Summary 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Digital File Characteristics text file
PDF
Source of Description Online resource; title from PDF title page (SpringerLink, viewed November 9, 2021).
Added Author Lutz, Carl O. R., author.
Pottmann, Helmut, author.
Techter, Jan, author.
Series SpringerBriefs in mathematics.
Available in Other Form Non-Euclidean Laguerre geometry and incircular nets.
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All Resources
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.

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