Singularities of Non-Developable Ruled Surface with Spacelike Ruling

In this paper, we study singularities of the spherical indicatrix and evolute of spacelike ruled surface with spacelike ruling. Finally, we give an example to illustrate our results.

ON SURFACES CONSTRUCTED BY EVOLUTION ACCORDING TO QUASI FRAME

The present paper presents evolutions of spherical indicatrix of a space curve according to the quasi-frame. Then, some geometric properties of these surfaces constructed by evolutions have been obtained. At the end, illustrative examples of the spherical images of a space curve have been presented.

TIMELIKE SURFACES OF EVOLUTION IN MINKOWSKI 3-SPACE

The present paper presents evolution of spherical indicatrix of a space curve according to the quasi frame in Minkowski 3-space. Some geometric properties such as fundamental forms and curvatures of the surfaces constructed by evolutions are obtained.

Directional spherical indicatrices of timelike space curve

In this work, the directional spherical indicatrices of a timelike space curve using tangent, quasi-normal and quasi-binormal vectors with q-frame are introduced. Then we work on the condition, that a timelike space curve to be slant helix, by using the geodesic curvature of the directional normal spherical indicatrix. Finally, an application of the results is given.

A study on timelike circular surfaces in Minkowski 3-space

This paper studies a smooth one-parameter family of standard Lorentzian circles with fixed radius. Such a surface is called a timelike circular surface with constant radius. We call each circle a generating circle. A new type of timelike circular surfaces was identified and coined as the timelike tangent circular surface. The new timelike tangent circular surface has the property of all generating circles being lines of curvature and its Gaussian and mean curvatures being independent of the geodesic curvature of the spherical indicatrix.

On Energies of Charged Particles with Magnetic Field

The present paper is about magnetic curves of spherical images in Euclidean 3-space. We obtain the Lorentz forces of the spherical images and then we determine if the spherical images have a magnetic curve or not. If a spherical image has a magnetic curve, then after presenting some basic concepts about the energy of a charged particle whose trajectory is that magnetic curve and the kinetic energy of a moving particle whose trajectory is the spherical indicatrix, we find the energy of the charged particle and the kinetic energy of the moving particle.