New Kind Frenet Curves in Minkowski Space

Abstract

In this study, we define new vector fields along a Frenet curve with nonvanishing curvatures in 4-dimensional Minkowski space R^4_1 . By using these vector fields we obtain some new planes and curves. We show that these planes play the role of the Darboux vector. We characterized that, osculating curves of the first kind and rectifying curves in Minkowski space R^4_1 can be given as space curves whose position vectors always lie in a two-dimensional subspace.

Keywords

• Frenet curve
• Darboux vector
• Rectifying curve

References

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