Non-Euclidean Laguerre Geometry and Incircular Nets
1st ed. 2021
Book Details
Format
Paperback / Softback
Book Series
SpringerBriefs in Mathematics
ISBN-10
3030818462
ISBN-13
9783030818463
Edition
1st ed. 2021
Publisher
Springer Nature Switzerland AG
Imprint
Springer Nature Switzerland AG
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Oct 30th, 2021
Print length
137 Pages
Product Classification:
Non-Euclidean geometry
Ksh 9,900.00
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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.
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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