Special helices on equiform differential geometry of timelike curves in 𝔼𝟏 �

Abstract

In this paper, we introduce the moving Frenet frame along the timelike curve in 𝔼1 4 and then Frenet formulas with the equiform parameter in the equiform geometry of the Minkowski space-time. We obtain 𝑘-type helices for equiform differential geometry of timelike curves in Minkowski space-time 𝔼1 4 , in terms of their curvature functions. We give some new characterizations for these helices and investigate the special helices in Minkowski space-time. Finally, we establish (𝑘, 𝑚)-type slant helices for equiform differential geometry of timelike curves in 𝔼1 4 .