Curves with constant curvature ratios

Abstract

Curves in ${\mathbb{R}}^n$ 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.

Cited by in corpus (7)

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• New special curves and their spherical indicatrices
• Some Characterizations of Slant Helices in the Euclidean Space E^n
• Determination of the position vectors of general helices from intrinsic equations in $\e^3$
• Similar Curves With Variable Transformations
• Osculating direction curves and their applications
• Some Characterizations of Special Curves in the Euclidean Space ${\mathrm{E}}^4$