Mathematics > Differential Geometry
[Submitted on 29 Nov 2024]
Title:Differential geometry of curves in dual space
View PDF HTML (experimental)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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