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Abstract:In this paper, we study the position vectors of a timelike curve in the Minkowski 3-space R 3 1 . We give some characterizations for timelike curves which lie on some subspaces of R 3 1 .

In this paper by establishing the Frenet frame fT; N; B 1 ; B 2 g for a spacelike curve we give some characterizations for the spacelike inclined curves and B 2-slant helices in R 4 2 .

In this article, we characterize interpolating sesqui-harmonic spacelike curves in a fourdimensional conformally and quasi-conformally flat and conformally symmetric Lorentzian Para-Sasakian manifold. We give some theorems for these curves.

In this paper by establishing the Frenet frame for a timelike curve we study the different position vectors of timelike curves in Semi-Euclidean space. We gave the position vectors of timelike curves in terms of curvature functions which lie on the three dimensional subspaces of .

<abstract><p>In this paper, we give some characterizations of Frenet curves in 3-dimensional $ \delta $-Lorentzian trans-Sasakian manifolds. We compute the Frenet equations and Frenet elements of these curves. We also obtain the curvatures of non-geodesic Frenet curves on 3-dimensional $ \delta $-Lorentzian trans-Sasakian manifolds. Finally, we give some results for these curves.</p></abstract>

In this paper, we give some characterizations of Frenet curves in 3-dimensional contact Lorentzian Manifolds. We define Frenet equations and the Frenet elements of these curves. We also obtain the curvatures of non-geodesic Frenet curves on 3-dimensional contact Lorentzian Manifolds. Finally we give some corollaries and examples for these curves.