Distinguishing characteristics of equiform Hasimoto surfaces in Minkowski 3-space

Abstract

We investigate the equiform Hasimoto surfaces P(σ, ℓ) in Minkowski 3-space in this paper. In E 3 1 , in different three cases, the geometric properties of equiform Hasimoto surfaces are discussed. For each case, the equiform Gaussian and mean curvatures of the equiform Hasimoto surface are determined. Then, in E 3 1 , we characterize the parameter equiform Bishop curves of equiform Hasimoto surfaces. Keywords— Hasimoto surface, Minkowski geometry, equiform Bishop frame, smoke ring equation.