scholarly journals Surfaces in Laguerre geometry

2019 ◽  
Vol 117 ◽  
pp. 223-255 ◽  
Author(s):  
Emilio Musso ◽  
Lorenzo Nicolodi
Keyword(s):  
Laguerre Geometry

Voronoi Diagram in the Laguerre Geometry and Its Applications

1985 ◽  
Vol 14 (1) ◽  
pp. 93-105 ◽  
Author(s):  
Hiroshi Imai ◽  
Masao Iri ◽  
Kazuo Murota
Keyword(s):  
Voronoi Diagram ◽  
Laguerre Geometry

Laguerre Geometry of Surfaces in R 3

2005 ◽  
Vol 21 (6) ◽  
pp. 1525-1534 ◽  
Author(s):  
Tong Zhu Li
Keyword(s):  
Laguerre Geometry

scholarly journals Laguerre geometries and some connections to generalized quadrangles

2007 ◽  
Vol 83 (3) ◽  
pp. 335-356
Author(s):  
Matthew R. Brown
Keyword(s):  
Three Dimensional ◽  
Line Pair ◽  
Generalized Quadrangles ◽  
Constant Number ◽  
Unique Point ◽  
Line Geometry ◽  
Laguerre Geometry ◽  
Point Line ◽  
Dimensional Projective Space ◽  
Unique Circle

AbstractA Laguerre plane is a geometry of points, lines and circles where three pairwise non-collinear points lie on a unique circle, any line and circle meet uniquely and finally, given a circle C and a point Q not on it for each point P on C there is a unique circle on Q and touching C at P. We generalise to a Laguerre geometry where three pairwise non-collinear points lie on a constant number of circles. Examples and conditions on the parameters of a Laguerre geometry are given.A generalized quadrangle (GQ) is a point, line geometry in which for a non-incident point, line pair (P. m) there exists a unique point on m collinear with P. In certain cases we construct a Laguerre geometry from a GQ and conversely. Using Laguerre geometries we show that a GQ of order (s. s2) satisfying Property (G) at a pair of points is equivalent to a configuration of ovoids in three-dimensional projective space.

scholarly journals A Generalization of Laguerre Geometry 1.

1951 ◽  
Vol 2 (3-4) ◽  
pp. 253-266
Author(s):  
Yasuro TOMONAGA
Keyword(s):  
Laguerre Geometry
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