Non-Euclidean Laguerre geometry and incircular nets /: Alexander I. Bobenko, Carl O.R. Lutz, Helmut Pottmann, Jan Techter.

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

doi:10.1007/978-3-030-81847-0

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

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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

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.

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Includes bibliographical references and index.

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Access limited to authorized users.

Digital File Characteristics

text file
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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.