| Non-Euclidean Laguerre Geometry and Incircular Nets 2021 Edition Contributor(s): Bobenko, Alexander I. (Author), Lutz, Carl O. R. (Author), Pottmann, Helmut (Author) |
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ISBN: 3030818462 ISBN-13: 9783030818463 Publisher: Springer OUR PRICE: $66.49 Product Type: Paperback Published: October 2021 |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Non-euclidean |
| Physical Information: 0.32" H x 6.14" W x 9.21" (0.48 lbs) 137 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |