In this work, we define the tangent spherical image of a unit speed time-like curve lying on the pseudohyperbolic space H 2 0 (r) in L 3 . In addition, we calculate a ccr-curve of this curve in L 3 . Besides, we determine a relation between harmonic curvature and a ccr-curve in L 3 , and so we obtain some new results.
In this paper, we find a relation between Frenet formulas and harmonic curvatures, and also a relation between Frenet formulas and e-curvature functions of a curve of osculating order 6 in 6 dimensional Lorentzian space L 6. Moreover, we give a relation between harmonic curvatures and ccr-curves of a curve in L 6 .
In this paper, we study with Frenet equations which are given in  of a partially null curve in Semi-Euclidean 4-space E 4 2 with index 2. By using the Frenet equations, we give some theorem and corollary. A characterization of a hyperbolic partially null curve in E 4 2 is given. Additionally, we examine harmonic curvatures and curvatures of this curve in E 4 2 .
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