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＜E-Book＞
Non-Euclidean Laguerre Geometry and Incircular Nets / by Alexander I. Bobenko, Carl O.R. Lutz, Helmut Pottmann, Jan Techter
(SpringerBriefs in Mathematics. ISSN:21918201)

Edition	1st ed. 2021.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2021
Size	X, 137 p. 57 illus., 53 illus. in color : online resource
Authors	*Bobenko, Alexander I author Lutz, Carl O.R author Pottmann, Helmut author Techter, Jan author SpringerLink (Online service)
Subjects	LCSH:Geometry LCSH:Projective geometry LCSH:Geometry, Hyperbolic FREE:Geometry FREE:Projective Geometry FREE:Hyperbolic Geometry
Notes	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 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 HTTP:URL=https://doi.org/10.1007/978-3-030-81847-0

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