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arXiv · 2411.19494

Differential geometry of curves in dual space

Rafael López
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Abstract

We introduce the Frenet theory of curves in dual space $\d^3$. After defining the curvature and the torsion of a curve, we classify all curves in dual plane with constant curvature. We also establish the fundamental theorem of existence in the theory of dual curves, proving that there is a dual curve with prescribed curvature and torsion. Finally we classify all dual curves with constant curvature and torsion.

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Rafael López. 2024-11-29. Differential geometry of curves in dual space. https://arxiv.org/abs/2411.19494

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