Abstract
Using a special conformai map between the two-dimensional sphere and the extended plane, we describe some classes of curves on the sphere. We also discuss a differential geometric invariant determining a plane curve up to a direct similarity and study self-similar plane curves.
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Encheva, R., Georgiev, G. Curves on the shape sphere. Results. Math. 44, 279–288 (2003). https://doi.org/10.1007/BF03322987
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DOI: https://doi.org/10.1007/BF03322987