Malaysian Journal of Mathematical Sciences, May 2018, Vol. 12, No. 2
A Characterization of Non-Lightlike Curves With Respect to Parallel Transport Frame in Minkowski Space-Time
Buyukkutuk, S., Kişi, I., and Ozturk, G.
Corresponding Email: sezgin.buyukkutuk@kocaeli.edu.tr
Received date: 24 May 2017
Accepted date: 26 May 2018
Abstract:
In this paper, we characterize non-ligtlike curves \((x(s) = m_0(s)T(s) + m_1(s)M_1(s) + m_2(s)M_2(s) + m_3(s)M_3(s))\) in terms of their curvature functions \(m_i(s) (i = 0,1,2,3)\) with the help of parallel transport frame \(\left \{T,M_1,M_2,M_3\right \}\). We obtain a result about spacelike constant ratio curves. We give the necessary and sufficient conditions for such curves to be \(T\)-constant and \(N\)-constant of first and second kind. Also, we give the necessary and sufficient conditions for \(T\)-constant curves to lie on a Lorentzian sphere.
Keywords: Parallel transport frame, position vector, constant ratio curves
