In this paper, we mainly investigate (contra) pedals and (anti) orthotomics of frontals in the
de Sitter 2‐space from the viewpoint of singularity theory and differential geometry. We …

In this study, we consider framed curves as regular or singular space curves with an adapted
frame in Euclidean 3-space. We define framed natural mates of a framed curve that are …

In this paper, we define pedal and contrapedal curves of framed immersions, which can
have singularities, in the Euclidean 3-space and investigate the sufficient conditions that …

In this paper, we define framed slant helices and give a necessary and sufficient condition
for them in three-dimensional Euclidean space. Then, we introduce the spherical images of …

We consider the differential geometry of evolutes of singular curves and give the definitions
of spacelike fronts and timelike fronts in the Minkowski plane. We also give the notions of …

We define involutes and contrapedal curves of spherical curves and investigate some
properties. We also give the classifications of the singular points of involutes. Moreover, we …

In this study, we introduce framed clad helices, which are a generalization of clad (ie C-slant
or 2-slant) helices in Euclidean 3-space. They also include framed helices and framed slant …

In plane, the caustic by reflection of a curve mirror with respect to a light source is the
envelope of the rays, emitted from the light source, after reflection in the mirror. By this …

Using the technique of pedal coordinates we investigate the orbits of a free double linkage.
We provide a geometrical construction for them and also show a surprising connection …

We define ϕ-enveloids for one-parameter families of spherical Legendre curves. The ϕ-
enveloids are not only the generalizations of isogonal trajectories of regular spherical curves …