Evolutes and Involutes of Frontals in the Euclidean Plane
TLDR
In this article, the authors defined the evolutes and the involutes of frontals under conditions and gave an existence condition of the evolute with inflection points, which is a generalisation of both evo-forms of regular curves and of fronts.Abstract:
We have already defined the evolutes and the involutes of fronts without inflection points. For regular curves or fronts, we can not define the evolutes at inflection points. On the other hand, the involutes can be defined at inflection points. In this case, the involute is not a front but a frontal at inflection points. We define evolutes of frontals under conditions. The definition is a generalisation of both evolutes of regular curves and of fronts. By using relationship between evolutes and involutes of frontals, we give an existence condition of the evolute with inflection points. We also give properties of evolutes and involutes of frontals.read more
Citations
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Proceedings ArticleDOI
Singularities of frontals
TL;DR: In this article, the authors introduce the notion of frontals, which provides a class of generalised submanifolds with singularities but with well-defined tangent spaces.
Journal ArticleDOI
Dualities and evolutes of fronts in hyperbolic and de Sitter space
Liang Chen,Masatomo Takahashi +1 more
TL;DR: In this paper, the authors considered the differential geometry of evolutes of singular curves in hyperbolic 2-space and de Sitter 2-spaces, respectively, and studied the geometric properties of these evolutions.
Journal ArticleDOI
Primitivoids of curves in Minkowski plane
TL;DR: In this article , the authors investigated the differential geometric characteristics of pedal and primitive curves in a Minkowski plane, where a primitive is specified by the opposite structure for creating the pedal, and primitivoids are known as comparatives of the primitive of a plane curve.
Journal ArticleDOI
Involutes of fronts in the Euclidean plane
TL;DR: For a regular plane curve, an involute of it is the trajectory described by the end of a stretched string unwinding from a point of the curve as discussed by the authors, and the involute always has a singularity.
Journal ArticleDOI
On (contra)pedals and (anti)orthotomics of frontals in de Sitter 2‐space
Yanlin Li,O. Oğulcan Tuncer +1 more
TL;DR: In this article , the de Sitter Legendrian Frenet frames were used to provide parametric representations of (contra)pedal curves of spacelike and timelike frontals in the deSitter 2-space and to investigate the geometric and singularity properties of these (contraspedal) curves.
References
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Journal ArticleDOI
Singularities of differentiable maps
TL;DR: In this article, the authors present a set of conditions générales d'utilisation of commercial or impression systématique, i.e., the copie ou impression de ce fichier doit contenir la présente mention de copyright.
Book
Modern Differential Geometry of Curves and Surfaces with Mathematica
TL;DR: Modern Differential Geometry of Curves and Surfaces with Mathematica explains how to define and compute standard geometric functions, for example the curvature of curves, and presents a dialect ofMathematica for constructing new curves and surfaces from old.
Journal ArticleDOI
Curves and singularities, by J. W. Bruce and P. J. Giblin. Pp 222. 1984. ISBN 0-521-24945-7 (Hardback) £25, 27091-X (Paperback) £8·95 (Cambridge University Press)
Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition
TL;DR: The second edition of Modern Differential Geometry of Curves and Surfaces with Mathematica as mentioned in this paper combines a traditional approach with thesymbolic manipulation abilities of mathematica to explain and develop the classical theory of curves and surfaces.