Abstract
A framed curve is a smooth curve in the Euclidean space with a moving frame. We call the smooth curve in the Euclidean space the framed base curve. In this paper, we give an existence condition of framed curves. Actually, we construct a framed curve such that the image of the framed base curve coincides with the image of a given smooth curve under a condition. As a consequence, polygons in the Euclidean plane can be realised as not only a smooth curve but also a framed base curve.
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Fukunaga, T., Takahashi, M. Existence conditions of framed curves for smooth curves. J. Geom. 108, 763–774 (2017). https://doi.org/10.1007/s00022-017-0371-5
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DOI: https://doi.org/10.1007/s00022-017-0371-5