Characterization of spherical and plane curves using rotation minimizing frames

Luiz C. B. da Silva

doi:10.5269/bspm.49075

Autores

Luiz C. B. da Silva Weizmann Institute of Science http://orcid.org/0000-0002-2702-9976

DOI:

https://doi.org/10.5269/bspm.49075

Resumo

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.

Biografia do Autor

Luiz C. B. da Silva, Weizmann Institute of Science

Postdoctoral fellow at the Department of Physics of Complex Sytems.

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