Journal of Geometry

, Volume 108, Issue 1, pp 195–214 | Cite as

Evolutes of plane curves and null curves in Minkowski 3-space

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Abstract

We use the isotropic projection of Laguerre geometry in order to establish a correspondence between plane curves and null curves in the Minkowski 3-space. We describe the geometry of null curves (Cartan frame, pseudo-arc parameter, pseudo-torsion, pairs of associated curves) in terms of the curvature of the corresponding plane curves. This leads to an alternative description of all plane curves which are Laguerre congruent to a given one.

Keywords

Laguerre geometry Minkowski space null curves plane curves evolutes associated pairs of curves 

Mathematics Subject Classification

53A04 53A35 53B30 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Instituto Superior de Ciências da EducaçãoLubangoAngola
  2. 2.Departamento de MatemáticaUniversidade da Beira InteriorCovilhãPortugal

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