On the harmonic evolute of time-like Hasimoto surfaces in Lorentz–Minkowski space

Abstract

The movement of a thin vortex in a thin viscous fluid by the motion of a curve propagating in Lorentz–Minkowski space [Formula: see text] is described by the vortex filament or smoke ring equation and can be viewed as a dynamical system on the space curves in [Formula: see text]. This paper investigates the harmonic evolute surfaces of time-like Hasimoto surfaces in [Formula: see text]. Also, we discuss the geometric properties of these surfaces, namely, we obtain the Gaussian and mean curvatures of the first and second fundamental forms. As a verification, we construct a concrete example for the meant surfaces to demonstrate our theoretical results.