On some special curves in Lorentz-Minkowski plane

Abstract

Here we consider the plane curves whose curvature κ depends on the distance from the origin in Lorentz-Minkowski plane 𝔼12. We obtain their explicit parameterizations in the cases when the plane curves have curvatures which are linear or quadratic functions of the distance of their points from the origin in 𝔼12 up to a real positive multiplier σ ∈ ℝ+. We have derived also the algebraic equations which are uniformized by these parameterziations.

Keywords

• curvature
• plane curves