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Evolutes of fronts in the Euclidean plane

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84172

Title: Evolutes of fronts in the Euclidean plane
Authors: Fukunaga, Tomonori Browse this author
Takahashi, Masatomo Browse this author
Keywords: evolute
parallel curve
front
Legendre immersion
Issue Date: 17-Dec-2012
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 1026
Start Page: 1
End Page: 17
Abstract: The 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.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69831
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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