國立虎尾科技大學 |

Non-Euclidean Laguerre Geometry and Incircular Nets

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Non-Euclidean Laguerre Geometry and Incircular Nets/ by Alexander I. Bobenko, Carl O.R. Lutz, Helmut Pottmann, Jan Techter.
Author:	Bobenko, Alexander I.
other author:	Lutz, Carl O.R.
Description:	X, 137 p. 57 illus., 53 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Geometry. -
Online resource:	https://doi.org/10.1007/978-3-030-81847-0
ISBN:	9783030818470

Non-Euclidean Laguerre Geometry and Incircular Nets
Bobenko, Alexander I.

Non-Euclidean Laguerre Geometry and Incircular Nets[electronic resource] /by Alexander I. Bobenko, Carl O.R. Lutz, Helmut Pottmann, Jan Techter. - 1st ed. 2021. - X, 137 p. 57 illus., 53 illus. in color.online resource. - 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 Möbius 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:

579899
Geometry.

LC Class. No.: QA440-699

Dewey Class. No.: 516

Non-Euclidean Laguerre Geometry and Incircular Nets
LDR:02614nam a22003975i 4500 001 1056747
003 DE-He213
005 20211029173224.0
007 cr nn 008mamaa
008 220103s2021 sz | s |||| 0|eng d
020 $a 9783030818470 $9 978-3-030-81847-0
024 7 $a 10.1007/978-3-030-81847-0 $2 doi
035 $a 978-3-030-81847-0
050 4 $a QA440-699
072 7 $a PBM $2 bicssc
072 7 $a MAT012000 $2 bisacsh
072 7 $a PBM $2 thema
082 0 4 $a 516 $2 23
100 1 $a Bobenko, Alexander I. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 679615
245 1 0 $a Non-Euclidean Laguerre Geometry and Incircular Nets $h [electronic resource] / $c by Alexander I. Bobenko, Carl O.R. Lutz, Helmut Pottmann, Jan Techter.
250 $a 1st ed. 2021.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a X, 137 p. 57 illus., 53 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a SpringerBriefs in Mathematics, $x 2191-8201
505 0 $a 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.
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.
650 0 $a Geometry. $3 579899
650 0 $a Projective geometry. $3 1255393
650 0 $a Hyperbolic geometry. $3 1264371
650 2 4 $a Projective Geometry. $3 1021390
650 2 4 $a Hyperbolic Geometry. $3 1069789
700 1 $a Lutz, Carl O.R. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1362102
700 1 $a Pottmann, Helmut. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1362103
700 1 $a Techter, Jan. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1362104
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030818463
776 0 8 $i Printed edition: $z 9783030818487
830 0 $a SpringerBriefs in Mathematics, $x 2191-8198 $3 1255329
856 4 0 $u https://doi.org/10.1007/978-3-030-81847-0
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)