Characterizations of Hasimoto Surfaces in Euclidean 3-spaces E3

Abstract

The position vector of the surface r = r(s, t) is called Hasimoto surface if the relation rt = rs ∧ rss hold. In this paper Hasimoto surfaces in Euclidean space E3 will be introduced. Hasimoto surfaces are investigated by using the Darboux frame and discuss the geometric properties. The position vector ofW-curve is stated by a linear combination of its Frenet frame with differentiable functions.