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Non-Euclidean Laguerre Geometry and Incircular Nets
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Catalogue Information
Field name
Details
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
Links to Related Works
Subject References:
Geometry
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Geometry, Hyperbolic
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Hyperbolic Geometry
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Projective Geometry
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Authors:
author
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Bobenko, Alexander I.
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Lutz, Carl O.R.
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Pottmann, Helmut
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Techter, Jan
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Corporate Authors:
SpringerLink (Online service)
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Series:
SpringerBriefs in Mathematics
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Classification:
516
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