Position vectors of a spacelike $W$-curve in Minkowski space $Bbb{E}^3_1$
Bull. Korean Math. Soc. 2007 Vol. 44, No. 3, 429-438
Printed September 1, 2007
Kazim Ilarslan and Ozgur Boyaciouglu
Ki ri kkale University, Kocatepe University
Abstract : In this paper, we study the position vectors of a spacelike $W$-curve (or a helix), i.e., curve with constant curvatures, with spacelike, timelike and null principal normal in the Minkowski 3-space $\Bbb{E}^{3}_{1}$. We give some chracterizations for spacelike $W$- curves whose image lies on the pseudohyperbolical space $\Bbb{H}^{2}_{0}$ and Lorentzian sphere $\Bbb{S}^{2}_{1}$ by using the positions vectors of the curve.
Keywords : spacelike curve, $W$-curve, normal curve, position vector, Minkowski space
MSC numbers : 53C50, 53C40
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