Abstract
In this article Hasimoto surfaces in Galilean space G_{3} will be considered, Gauss curvature (K) and Mean curvature (H) of Hasimoto surfaces chi =chi (s,t) will be investigated, some characterization of s-curves and t-curves of Hasimoto surfaces in Galilean space G_{3} will be introduced. Example of Hasimoto surfaces will be illustrated.
Highlights
The geometry of Galilean is one of the Non Euclidean geometry which is very important in special Relativity
The Galilean geometry is the geometry that is transferred from Euclidean geometry to special relativity
Hasimoto surfaces are obtained when the motions of local speed of the curve is proportional to the local curvature of the curve
Summary
Some conditions for the s-parameter curves and t-parameter curves of Hasimoto surfaces to be geodesic curves, or asymptotic lines in Galilean space G3 will be given. Lines, which do not cross the absolute line f is called proper non-isotropic lines. 2. The lines, which not belong to the ideal plane ω but intersect the absolute line f is called the proper isotropic lines. 3. All lines of the ideal plane ω except f are called proper non-isotropic lines. K(s) is called the curvature function of the admissible curve r(s), and is denoted by the relation k(s) = y′′2 + z′′2 and τ (s) is the torsion function of the admissible curve r(s) and is given by the following equation.
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