• Corpus ID: 229157271

Pedal curves, orthotomics and catacaustics of frontals in the hyperbolic 2-space

@article{Tuncer2020PedalCO,
  title={Pedal curves, orthotomics and catacaustics of frontals in the hyperbolic 2-space},
  author={O. Ogulcan Tuncer and Ismail Gok},
  journal={arXiv: Differential Geometry},
  year={2020}
}
In this paper, firstly the definition of the pedal curves of spacelike frontals is presented. The parametric representation of pedal curves of spacelike frontals is given by using the hyperbolic Legendrian moving frames along these frontals. We mainly deal with the classification and recognition problems of singularities of hyperbolic pedal curves of spacelike frontals constructed by non-singular and singular dual curve germs in hyperbolic 2-space. We show that for non-singular dual curve germs… 

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References

SHOWING 1-10 OF 31 REFERENCES
Pedal curves of fronts in the sphere
Notions of the pedal curves of regular curves are classical topics. T. Nishimura [T. Nishimura, Demonstratio Math., 43 (2010), 447–459] has done some work associated with the singularities of pedal
Notes on pedal and contrapedal curves of fronts in the Euclidean plane
A pedal curve (a contrapedal curve) of a regular plane curve is the locus of the feet of the perpendiculars from a point to the tangents (normals) to the curve. These curves can be parametrized by
Normal forms for singularities of pedal curves produced by non-singular dual curve germs in Sn
For an n-dimensional spherical unit speed curve r and a given point P, we can define naturally the pedal curve of r relative to the pedal point P. When the dual curve germs are non-singular,
Dualities and evolutes of fronts in hyperbolic and de Sitter space
SINGULARITIES OF PEDAL CURVES PRODUCED BY SINGULAR DUAL CURVE GERMS IN Sn
For an n-dimensional spherical unit speed curve r and a given point P, we can define naturally the pedal curve of r relative to the pedal point P. When the dual curve germs are singular, singularity
Framed curves in the Euclidean space
Abstract A framed curve in the Euclidean space is a curve with a moving frame. It is a generalization not only of regular curves with linear independent condition, but also of Legendre curves in the
Involutes of fronts in the Euclidean plane
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. Even for a regular curve, the involute always has a
Projections of surfaces in the hyperbolic space to hyperhorospheres and hyperplanes
We study in this paper orthogonal projections in a hyperbolic space to hyperhorospheres and hyperplanes. We deal in more details with the case of embedded surfaces $M$ in $H^3_+(-1)$. We study the
Existence and uniqueness for Legendre curves
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
Pedal curves of frontals in the Euclidean plane
In this paper, we will give the definition of the pedal curves of frontals and investigate the geometric properties of these curves in the Euclidean plane. We obtain that pedal curves of frontals in
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