Non-Euclidean Laguerre Geometry and Incircular Nets / by Alexander I. Bobenko, Carl O.R. Lutz, Helmut Pottmann, Jan Techter

By:

Bobenko, Aleksandr I, 1960- [VerfasserIn]

Contributor(s):

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerBriefs in Mathematics | Springer eBook CollectionPublisher: Cham : Springer, 2021Description: 1 Online-Ressource (X, 137 p. 57 illus., 53 illus. in color.)ISBN:

9783030818470

Subject(s):

Additional physical formats: 9783030818463 | 9783030818487 | Erscheint auch als: 9783030818463 Druck-Ausgabe | Erscheint auch als: 9783030818487 Druck-Ausgabe | Erscheint auch als: Non-Euclidean Laguerre geometry and incircular nets. Druck-Ausgabe Cham, Switzerland : Springer Nature, 2021. x, 137 SeitenDDC classification:

516 23

DOI: DOI: 10.1007/978-3-030-81847-0Online resources:

Summary: Introduction -- Two-dimensional non-Euclidean Laguerre geometry -- Quadrics in projective space -- Cayley-Klein spaces -- Central projection of quadrics and Möbius geometry -- Non-Euclidean Laguerre geometry -- Lie geometry -- Checkerboard incircular nets -- Euclidean cases -- Generalized signed inversive distance.Summary: 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.PPN: PPN: 177586538XPackage identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS

Holdings ( 0 )

No physical items for this record