IJPAM: Volume 16, No. 1 (2004)

THE CHARACTERIZATIONS FOR HELICES
IN THE GALILEAN SPACE $G_{3}$

A.O. Ögrenmis$^1$, M. Bektas$^2$, M. Ergüt$^3$
$^{1,2,3}$Department of Mathematics
Firat University
23119 Elazig, TURKEY
$^1$e-mail: aogrenmis@firat.edu.tr
$^2$e-mail: mbektas@firat.edu.tr
$^3$e-mail: mergut@firat.edu.tr


Abstract.In [4] T. Ikawa obtained a ordinary differential equation for the circular helix. Recently, the helix are investigated by many differential geometers such as [1], [2], [4]. Furthermore N. Ekmekçi and K. Ilarslan obtained characterizations of timelike null helices in terms of principal normal or binormal vector fields [3]. In this paper, we obtained characterizations of helices in terms of principal normal vector fields and another two characterizations for a curve with respect to the Frenet frame in 3-dimensional Galilean space $G_{3}$.

Received: June 11, 2004

AMS Subject Classification: 53B30

Key Words and Phrases: Galilean space, helix

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 16
Issue: 1