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

Boaventura Nolasco; Rui Pacheco

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arXiv · 1605.02117

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

Boaventura Nolasco·Rui Pacheco

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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.

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BibTeX RIS

Boaventura Nolasco, Rui Pacheco. 2016-05-06. Evolutes of plane curves and null curves in Minkowski $3$-space. https://arxiv.org/abs/1605.02117

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