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Non-Euclidean Laguerre geometry and ...

Bobenko, Alexander I.

Non-Euclidean Laguerre geometry and incircular nets

Record Type:	Electronic resources : Monograph/item
Title/Author:	Non-Euclidean Laguerre geometry and incircular netsby Alexander I. Bobenko ...[et al.].
other author:	Bobenko, Alexander I.
Published:	Cham :Springer International Publishing :2021.
Description:	x, 137 p. :ill. (chiefly col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Laguerre geometry.
Online resource:	https://doi.org/10.1007/978-3-030-81847-0
ISBN:	9783030818470$q(electronic bk.)

Non-Euclidean Laguerre geometry and incircular nets
Non-Euclidean Laguerre geometry and incircular nets[electronic resource] /by Alexander I. Bobenko ...[et al.]. - Cham :Springer International Publishing :2021. - x, 137 p. :ill. (chiefly col.), digital ;24 cm. - SpringerBriefs in mathematics,2191-8201. - SpringerBriefs in mathematics..

Introduction -- Two-dimensional non-Euclidean Laguerre geometry -- Quadrics in projective space -- Cayley-Klein spaces -- Central projection of quadrics and Mobius 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.

ISBN: 9783030818470$q(electronic bk.)

Standard No.: 10.1007/978-3-030-81847-0doiSubjects--Topical Terms:

908946
Laguerre geometry.

LC Class. No.: QA551

Dewey Class. No.: 516.3

Non-Euclidean Laguerre geometry and incircular nets
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245 0 0 $a Non-Euclidean Laguerre geometry and incircular nets $h [electronic resource] / $c by Alexander I. Bobenko ...[et al.].
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a x, 137 p. : $b ill. (chiefly col.), digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematics, $x 2191-8201
505 0 $a Introduction -- Two-dimensional non-Euclidean Laguerre geometry -- Quadrics in projective space -- Cayley-Klein spaces -- Central projection of quadrics and Mobius geometry -- Non-Euclidean Laguerre geometry -- Lie geometry -- Checkerboard incircular nets -- Euclidean cases -- Generalized signed inversive distance.
520 $a 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.
650 0 $a Laguerre geometry. $3 908946
650 0 $a Geometry, Non-Euclidean. $3 648181
650 0 $a Nets (Mathematics) $3 242536
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650 2 4 $a Hyperbolic Geometry. $3 684054
700 1 $a Bobenko, Alexander I. $3 277228
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830 0 $a SpringerBriefs in mathematics. $3 558795
856 4 0 $u https://doi.org/10.1007/978-3-030-81847-0
950 $a Mathematics and Statistics (SpringerNature-11649)