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<p>We introduce the Frenet theory of curves in dual space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {D}^3\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">D</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation>. 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.</p>

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Differential Geometry of Curves in Dual Space

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月23日

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  • Rafael López

摘要

We introduce the Frenet theory of curves in dual space \(\mathbb {D}^3\) 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.