株式会社極東書店トップ ＞ 商品一覧 ＞ Non-Euclidean Laguerre Geometry and Incircular Nets. 1st ed. 2021.
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Non-Euclidean Laguerre Geometry and Incircular Nets. 1st ed. 2021.
・ISBN 978-3-030-81846-3 paper EUR 64.99
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| 著者・編者 | Bobenko, Alexander I. / Lutz, Carl O.R. / Pottmann, Helmut / Techter, Jan, |
|---|---|
| シリーズ | SpringerBriefs in Mathematics |
| 出版社 | (Springer Nature Switzerland AG, SZ) |
| 出版年月 | 2021 |
| ページ数 | 137 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-7454＞ |
解説
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.
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.