Existence and uniqueness for Legendre curves
TLDR
In this article, the authors give a moving frame of a Legendre curve (or, a frontal) in the unit tangent bundle and define a pair of smooth functions of the curve like the curvature of a regular plane curve.Abstract:
We give a moving frame of a Legendre curve (or, a frontal) in the unit tangent bundle and define a pair of smooth functions of a Legendre curve like as the curvature of a regular plane curve. It is quite useful to analyse the Legendre curves. The existence and uniqueness for Legendre curves hold similarly to the case of regular plane curves. As an application, we consider contact between Legendre curves and the arc-length parameter of Legendre immersions in the unit tangent bundle.read more
Citations
More filters
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)
Journal ArticleDOI
Framed curves in the Euclidean space
TL;DR: In this paper, the curvature of a framed curve is defined, similarly to the curvatures of a regular curve and of a Legendre curve in the unit tangent bundle.
Journal ArticleDOI
Evolutes and Involutes of Frontals in the Euclidean Plane
TL;DR: 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.
Journal ArticleDOI
Tangent developables and Darboux developables of framed curves
Yanlin Li,Siyao Liu,Zhigang Wang +2 more
TL;DR: In this paper, the authors generalize the tangent developables of regular curves with linear independent condition to the Tangent Developables of framed curves and investigate the singularities of tangent developedables in Euclidean 3-space.
References
More filters
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.