Haytham. A. Ali | Searcharxiv

arXiv2022

Spacelike Curves of Constant-Ratio in Pseudo-Galilean Space

In the theory of differential geometry curves, a curve is said to be of constant-ratio if the ratio of the length of the tangential and normal components of its position vector function is constant. In this paper, we study and characterize a spacelike admissible curve of constant-ratio in terms of its curvature functions in pseudo-Galilean space. Some special curves of constant-ratio such as T and N constant types are investigated. As an application of our main results, some examples are given.

math.DG↗

arXiv2018

Affine Factorable Surfaces in Pseudo-Galilean Space

An affine factorable surface of the second kind in the three dimensional pseudo-Galilean space G13 is studied depending on the invariant theory and theory of differential equation. The first and second fundamental forms, Gaussian curvature and mean curvature of the meant surface are obtained according to the basic principles of differential geometry. Also, some special cases are presented by changing the partial differential equation into the ordinary differential equation to simplify the solving process. The classification theorems of the considered surface with zero and non zero Gaussian and mean curvatures are given. Some examples of such a study are provided

math.GM↗