In this work, we firstly introduce notions of principal directed curves and donor which are associated a Frenet curve in the dual Lorentzian space D 3 1 D13 . We give some relations between curvature torsion curve. show that general helix is plane obtain equation by using position vector Then circle $\mathbb{D}^{2}$ or hyperbola $\mathbb{D}_{1}^{2}$ slant $\mathbb{D}_{1}^{3}$ helix, respectivel...

We consider a unit speed curve α in Euclidean four-dimensional space E and denote the Frenet frame by {T,N,B1,B2}. We say that α is a slant helix if its principal normal vector N makes a constant angle with a fixed direction U . In this work we give different characterizations of such curves in terms of their curvatures. MSC: 53C40, 53C50

A slant weighted Toeplitz operator Aφ is an operator on L(β) defined as Aφ = WMφ where Mφ is the weighted multiplication operator and W is an operator on L(β) given by We2n = βn β2n en, {en}n∈Z being the orthonormal basis. In this paper, we generalise Aφ to the k-th order slant weighted Toeplitz operator Uφ and study its properties. Keywords—Slant weighted Toeplitz operator, weighted multiplica...

In this study, we introduce the natural mate and conjugate of a Frenet curve in three dimensional Lie group $ \mathbb{G} with bi-invariant metric. Also, give some relationships between its or $. Especially, obtain results for when is general helix, slant spherical curve, rectifying Salkowski (constant curvature non-constant torsion), anti-Salkowski (non-constant constant Bertrand curve. Finally...

Slant aftereffect (SAE), the negative aftereffect of slant induced after prolonged observation of a surface, is considered as evidence that slant is encoded in the visual system. Because slant and tilt are mathematically independent dimensions, Stevens (Stevens, K. A. (1983a). Biological Cybernetics, 46, 183-195) assumed that slant and tilt are processed independently in the visual system. To c...