2024-03-28T19:48:41Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/698922022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Existence conditions of framed curves for smooth curvesFukunaga, TomonoriTakahashi, Masatomo410A 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.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69892info:doi/10.14943/84232https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69892/1/pre1088.pdfHokkaido University Preprint Series in Mathematics10881102016-05-12engpublisher