Wentworth
Institute of Technology
Non-Euclidean Laguerre Geometry and Incircular Nets
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 checkerbo...
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| Main Authors: | , , , |
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| Corporate Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cham :
Springer International Publishing : Imprint: Springer,
2021.
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| Edition: | 1st ed. 2021. |
| Series: | SpringerBriefs in mathematics.
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| Subjects: | |
| Online Access: |
Full text (Wentworth users only) |
| 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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| Physical Description: | X, 137 pages 57 illustrations, 53 illustrations in color : online resource. |
| ISBN: | 9783030818470 |
| ISSN: | 2191-8201 |
| DOI: | 10.1007/978-3-030-81847-0 |