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Non-Euclidean Laguerre Geometry and Incircular Nets

Non-Euclidean Laguerre Geometry and Incircular Nets

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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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Tjek vores konkurrenters priser
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.


Produktdetaljer
Sprog: Engelsk
Sider: 137
ISBN-13: 9783030818463
Indbinding: Paperback
Udgave:
ISBN-10: 3030818462
Udg. Dato: 30 okt 2021
Længde: 0mm
Bredde: 155mm
Højde: 235mm
Forlag: Springer Nature Switzerland AG
Oplagsdato: 30 okt 2021
Forfatter(e) Helmut Pottmann, Jan Techter, Carl O.R. Lutz, Alexander I. Bobenko


Kategori Ikke-euklidisk geometri


ISBN-13 9783030818463


Sprog Engelsk


Indbinding Paperback


Sider 137


Udgave


Længde 0mm


Bredde 155mm


Højde 235mm


Udg. Dato 30 okt 2021


Oplagsdato 30 okt 2021


Forlag Springer Nature Switzerland AG

Kategori sammenhænge