Non-Euclidean Laguerre Geometry and Incircular Nets (Paperback, 1st ed. 2021)

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.

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Series:	SpringerBriefs in Mathematics
Release date:	October 2021
First published:	2021
Authors:	Alexander I. Bobenko • Carl O.R. Lutz • Helmut Pottmann • Jan Techter
Dimensions:	235 x 155mm (L x W)
Format:	Paperback
Pages:	137
Edition:	1st ed. 2021
ISBN-13:	978-3-03-081846-3
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Non-Euclidean geometry Promotions
LSN:	3-03-081846-2
Barcode:	9783030818463

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