2024-03-29T11:04:34Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/698312022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Evolutes of fronts in the Euclidean planeFukunaga, TomonoriTakahashi, Masatomoevoluteparallel curvefrontLegendre immersion410The evolute of a regular curve in the Euclidean plane is given by not only the caustics of the regular curve, envelope of normal lines of the regular curve, but also the locus of singular loci of parallel curves. In general, the evolute of a regular curve have singularities, since such a point is corresponding to a vertex of the regular curve and there are at least four vertices for simple closed curves. If we repeated an evolute, we cannot define the evolute at a singular point. In this paper, we define an evolute of a front and give properties of such evolute by using a moving frame of a front and the curvature of the Legendre immersion. As applications, repeated evolutes can be well-defined and these are useful to recognize the shape of curves.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69831info:doi/10.14943/84172https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69831/1/pre1026.pdfHokkaido University Preprint Series in Mathematics10261172012-12-17engpublisher