Differential geometry of curves in dual space

2024/11/29 by Rafael López, López, Rafael · 1 citation
Engineering · Computer Science · Mathematics · #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2411.19494

Abstract

We introduce the Frenet theory of curves in dual space \d³. 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.

Cited by

• Constant curvature curves in dual affine and dual Lorentz-Minkowski planes

Related

• A Survey of the Differential Geometry of Discrete Curves
• Constant curvature curves in dual affine and dual Lorentz-Minkowski planes
• Closed Constant Curvature Space Curves
• Normal and Spherical Curves in Dual Space
• Frenet Curves and Successor Curves: Generic Parametrizations of the Helix and Slant Helix