Non-Euclidean Laguerre geometry and incircular nets
Author(s)
Bibliographic Information
Non-Euclidean Laguerre geometry and incircular nets
（SpringerBriefs in mathematics）
Springer, c2021
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Note
Includes bibliographical references (p. 135-137)
Other authors: Carl O.R. Lutz, Helmut Pottmann, Jan Techter
Description and Table of Contents
Description
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.
Table of Contents
Introduction.- Two-dimensional non-Euclidean Laguerre geometry.- Quadrics in projective space.- Cayley-Klein spaces.- Central projection of quadrics and Moebius geometry.- Non-Euclidean Laguerre geometry.- Lie geometry.- Checkerboard incircular nets.- Euclidean cases.- Generalized signed inversive distance.
by "Nielsen BookData"
