| Dewey Class |
516 |
| Title |
Non-Euclidean Laguerre Geometry and Incircular Nets ([EBook] /) / by Alexander I. Bobenko, Carl O.R. Lutz, Helmut Pottmann, Jan Techter. |
| Author |
Bobenko, Alexander I. |
| Added Personal Name |
Lutz, Carl O.R. |
| Pottmann, Helmut |
| Techter, Jan |
| Other name(s) |
SpringerLink (Online service) |
| Edition statement |
1st ed. 2021. |
| Publication |
Cham : : Springer International Publishing : : Imprint: Springer, , 2021. |
| Physical Details |
X, 137 p. 57 illus., 53 illus. in color. : online resource. |
| Series |
SpringerBriefs in Mathematics 2191-8201 |
| ISBN |
9783030818470 |
| Summary Note |
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.: |
| Contents note |
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. |
| Mode of acces to digital resource |
Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). |
| Internet Site |
https://doi.org/10.1007/978-3-030-81847-0 |
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