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Non-Euclidean Laguerre geometry and ...

Bobenko, Alexander I.

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Non-Euclidean Laguerre geometry and incircular nets

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Non-Euclidean Laguerre geometry and incircular nets/ by Alexander I. Bobenko ...[et al.].
其他作者:	Bobenko, Alexander I.
出版者:	Cham :Springer International Publishing : : 2021.,
面頁冊數:	x, 137 p. :ill. (chiefly col.), digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Laguerre geometry. -
電子資源:	https://doi.org/10.1007/978-3-030-81847-0
ISBN:	9783030818470

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

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

3522331
Laguerre geometry.

LC Class. No.: QA551

Dewey Class. No.: 516.3

Non-Euclidean Laguerre geometry and incircular nets
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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.
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