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Laguerresche Differentialgeometrie und Kinematik

Zdeněk Jankovský (1995)

Mathematica Bohemica

In this paper the plane Laguerre’s geometry in the augmented plane of dual numbers is presented. Basic integral and differential invariants of -curves in the plane are deduced, i.e. the -curve arc, -curvature, -minimal curves, -circle. Furthermore the contact of -curves, -osculating circle, -evolute of a curve and some special -motions are studied from the point of view of -Differential geometry.

Legendrian dual surfaces in hyperbolic 3-space

Kentaro Saji, Handan Yıldırım (2015)

Annales Polonici Mathematici

We consider surfaces in hyperbolic 3-space and their duals. We study flat dual surfaces in hyperbolic 3-space by using extended Legendrian dualities between pseudo-hyperspheres in Lorentz-Minkowski 4-space. We define the flatness of a surface in hyperbolic 3-space by the degeneracy of its dual, which is similar to the case of the Gauss map of a surface in Euclidean 3-space. Such surfaces are a kind of ruled surfaces. Moreover, we investigate the singularities of these surfaces and the dualities...

Lorentzian isothermic surfaces and Bonnet pairs

M. A. Magid (2004)

Annales Polonici Mathematici

Lorentzian surfaces in Lorentz three-space are studied using an indefinite version of the quaternions. A classification theorem for Bonnet pairs in Lorentz three-space is obtained.

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