Year: 2022
Type: article
Abstract: In this work, we study plane and spherical curves in Euclidean and Lorentz-Minkowski 3-spaces by employing rotation minimizing (RM) frames. By conveniently writing the curvature and torsion for a curve on a sphere, we show how to find the angle between the principal normal and an RM vector field for spherical curves. Later, we characterize plane and spherical curves as curves whose position vector lies, up to a translation, on a moving plane spanned by their unit tangent and an RM vector field. Finally, as an application, we characterize Bertrand curves as curves whose so-called natural mates are spherical.
DOI: 10.5269/bspm.49075
Author: Luiz C. B. Da Silva
Institution: Weizmann Institute of Science
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Funder: Weizmann Institute of Science
OpenAlex ID: W2624769072