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Laguerre geometry of surfaces with plane lines of curvature
Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg, 1999 The authors continue their study of \(L\)-isothermic surfaces initiated in [the authors, New developments in differential geometry, Budapest 1996, 285-294 (1999; Zbl 0942.53006)]. Using moving frames, they find an integral formula for such surfaces and prove that an \(L\)-isothermic surface is \(L\)-congruent to either a cylindrical moulding surface ...
Lorenzo Nicolodi +2 more
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Applications of Laguerre geometry in CAGD
Computer Aided Geometric Design, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Helmut Pottmann, Martin Peternell
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Studying cyclides with Laguerre geometry
Computer Aided Geometric Design, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rimvydas Krasauskas, C. Mäurer
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Voronoi Diagram in the Laguerre Geometry and Its Applications
SIAM Journal on Computing, 1985The authors extend the concept of Voronoi diagram in the ordinary Euclidean geometry for n points to the one in the Laguerre geometry for n circles in the plane, where the distance between a circle and a point is defined by the length of the tangent line. Specifically, the distance \(d_ L(C_ i,P)\) between a circle \(C_ i\), with center \((x_ i,y_ i)\)
Masao Iri, Kazuo Murota
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Laguerre Geometry of Surfaces in R 3
Acta Mathematica Sinica, English Series, 2005Let f : M → R3 be an oriented surface with non–degenerate second fundamental form. We denote by H and K its mean curvature and Gauss curvature. Then the Laguerre volume of f, defined by L(f) = f (H2 – K)/KdM, is an invariant under the Laguerre transformations. The critical surfaces of the functional L are called Laguerre minimal surfaces. In this paper
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On the Equation Defining Isothermic Surfaces in Laguerre Geometry
, 1999 A surface f : M 2 → E 3 oriented by a unit normal field n induces a lift F = (f, n) to the space Λ = E 3 × S 2 of contact elements of E 3 which is a Legendre immersion with respect to the canonical contact structure of Λ. Λ is a homogeneous space of the 10-dimensional group L of Laguerre contact trasformations. These are transformations on the space of
MUSSO, EMILIO, L. NICOLODI
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Spinor Representation in Isotropic 3-Space via Laguerre Geometry
Results in Mathematics, 2023 We give a detailed description of the geometry of isotropic space, in parallel to those of Euclidean space within the realm of Laguerre geometry. After developing basic surface theory in isotropic space, we define spin transformations, directly leading ...
Joseph Cho, Dami Lee, Cho Joseph
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Two-Dimensional Laguerre Geometry
2021In this section we present two-dimensional Laguerre geometry in an elementary way, without reference to the following more general discussion, which begins in Chap. 3. We first introduce the most basic concepts of these geometries in the Euclidean plane and then turn to the elliptic and hyperbolic plane.
Alexander I. Bobenko +3 more
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2021
According to Felix Klein’s Erlangen program geometry is the study of invariants under a certain group of transformations. For example for Euclidean geometry this is the well-known Euclidean group. Analogously the less-known Laguerre geometry - which this thesis is dedicated to - is the study of invariants under the group of Laguerre transformations ...
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According to Felix Klein’s Erlangen program geometry is the study of invariants under a certain group of transformations. For example for Euclidean geometry this is the well-known Euclidean group. Analogously the less-known Laguerre geometry - which this thesis is dedicated to - is the study of invariants under the group of Laguerre transformations ...
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Non-Euclidean Laguerre Geometry
2021The primary objects in Mobius geometry are points on \(\mathcal {S}\), which yield a double cover of the points in hyperbolic/elliptic space, and spheres, which yield a double cover of the spheres in hyperbolic/elliptic space. The primary incidence between these objects is a point lying on a sphere.
Alexander I. Bobenko +3 more
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