The Chen type of Hasimoto surfaces in the Euclidean 3-space

Abstract

A surface $ \mathcal{M}^{2} $ with position vector $ r = r(s, t) $ is called a Hasimoto surface if the relation $ r_{t} = r_{s} \wedge r_{ss} $ holds. In this paper, we first define the Beltrami-Laplace operator according to the three fundamental forms of the surface, then we classify the $ J $-harmonic Hasimoto surfaces and their Gauss map in $ \mathbb{E}^{3} $, for $ J = II $ and $ III $.

Keywords

• hasimoto surface
• gauss map
• euclidean space
• beltrami-laplace operator
• surfaces of finite type