Yusuf Yayli

On slant helix and its spherical indicatrix

In this paper we investigate spherical images the tangent indicatrix and binormal indicatrix of a slant helix. We obtain that the spherical images are spherical helices. Moreover, we show that a curve of constant precession is a slant helix. For involute of a curve @c, we have obtain that @c is a slant helix if and only if its involute is a general helix.

Homothetic motions at E4

Abstract In this study, a Hamilton motion has been defined in four-dimensional Euclidean space E4, and it is shown that this is a homothetic motion. Furthermore, it has been found that the Hamilton motion defined by a regular curve of order r has only one acceleration centre of order (r−1) at every t-instant.

Slant helices in three dimensional Lie groups

In this paper, we define slant helices in three dimensional Lie groups with a bi-invariant metric and obtain a characterization of slant helices. Moreover, we give some relations between slant helices and their involutes, spherical images.

ON THE FERMI–WALKER DERIVATIVE AND NON-ROTATING FRAME

In this study Fermi–Walker derivative and according to the derivative Fermi–Walker parallelism and non-rotating frame concepts are given for some frames. First, we get the Frenet frame, the Darboux frame, the Bishop frame for any curve in Euclid space. Fermi–Walker derivative and non-rotating frame being conditions are analyzed for each of the frames along the curve. Then we proved the Frenet frame is non-rotating frame along the plane curves. Darboux frame which is a non-rotating frame along the line of curvature. Then we proved the Bishop frame is a non-rotating frame along the all curves.

A New Approach to Constant Slope Surfaces with Quaternions

We show a new method to construct constant slope surfaces with quaternions. Moreover, we give some results and illustrate an interesting shape of constant slope surfaces by using Mathematica.

MECHANICAL SYSTEMS ON GENERALIZED-QUATERNIONIC KÄHLER MANIFOLDS

In this paper, we introduce generalized-quaternionic Kahler analogue of Lagrangian and Hamiltonian mechanical systems. Finally, the geometrical-physical results related to generalized-quaternionic Kahler mechanical systems are also given.

A new approach for magnetic curves in 3D Riemannian manifolds

A magnetic field is defined by the property that its divergence is zero in a three-dimensional oriented Riemannian manifold. Each magnetic field generates a magnetic flow whose trajectories are curves called as magnetic curves. In this paper, we give a new variational approach to study the magnetic flow associated with the Killing magnetic field in a three-dimensional oriented Riemann manifold, (M3, g). And then, we investigate the trajectories of the magnetic fields called as N-magnetic and B-magnetic curves.

Time-Like Constant Slope Surfaces and Space-Like Bertrand Curves in Minkowski 3-Space

Defining Lorentzian Sabban frame of the unit speed time-like curves on de Sitter 2-space

On isophote curve and its characterizations

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