arXiv subjects

Ismail Gok

Publications and source records attributed to Ismail Gok.

3 recordsLinked to original sources

arXiv2020

Pedal curves of hyperbolic frontals and their singularities

This paper introduces pedal curves of spacelike frontals in the hyperbolic 2-space. We mainly investigate the singularities of these hyperbolic pedal curves of spacelike frontals for non-singular and singular dual curve germs. We then show that for non-singular dual curve germs, the singularities of a pedal curve are dependent on the singularities of the first hyperbolic Legendrian curvature germ and the location of the pedal point, while for singular dual curve germs, they depend upon the singularities of both hyperbolic Legendrian curvature germs and also the location of the pedal point. We provide several examples with figures.

math.DG↗

arXiv2014

Geometric Interpretation of det(C^(3),C^(4),C^(5))=0 in E13

In this paper, we investigate the tangent indicatrix of the curve C with constant curvature. Tangent indicatrix of the curve C is characterized with det(C^(3),C^(4),C^(5))=0 in Minkowski 3-space E13. Moreover, we study null slant helices using the determinant approach and give the following characterization: A curve C is a null slant helix in E13 if and only if det(C^(3),C^(4),C^(5))=0. Then similar results are obtained for non-null curves with the condition k=1.

math.DG↗

arXiv2013

A New Approach on Curves of Constant Precession

In this paper, we investigate a curve whose spherical image the tangent indicatrix and binormal indicatrix is slant helix and called it as a slant helix. We obtain that the spherical images are spherical slant helices defined by [3]. This notation is a generalization of a slant helix. Furthermore, we have given some characterizations for the slant helix and we show that a curve of constant precession is a slant helix.

math.DG↗