Curves with constant curvature ratios

2004/12/16 by J. Monterde, Monterde, J.
Mathematics · #53A04 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A04

paper · pdf · doi:10.48550/arxiv.math/0412323

arxiv created 2004/12/16 · arxiv updated 2009/12/01

Abstract

Curves in \mathbb Rⁿ for which the ratios between two consecutive curvatures are constant are characterized by the fact that their tangent indicatrix is a geodesic in a flat torus. For n= 3,4, spherical curves of this kind are also studied and compared with intrinsic helices in the sphere.

Related

• Intrinsic representation curves
• New special curves and their spherical indicatrices
• Direction curves of tangent indicatrix of a curve
• A New Approach on Curves of Constant Precession
• Spherical Indicatrices of Involute of a Space Curve in Euclidean 3-Space