Tbilisi Mathematical Journal

A study on spacelike rectifying curves in Minkowski 3-space

B. Doğan Yazici, S. Özkaldi Karakuş

In this paper, we investigate spacelike rectifying curves via dilation of unit speed spacelike or timelike curves on Lorentzian unit spheres in Minkowski 3-space E₁³. Then, we define a the centrode D_α(s) of a unit speed spacelike curve α(s) in E₁³. In last section, we prove that if a unit speed spacelike curve α(s) in E₁³ is neither a planar spacelike curve nor a helix, then its dilated centrode β(s)=ρ_α(s)D_α(s), with dilation factor ρ_α(s), is always a rectifying curve, where ρ_α(s) is the radius of curvature of α.


Tbilisi Mathematical Journal, Special Issue (IECMSA-2019), pp. 11-26