Geometry of Solutions of the Quasi-Vortex Filament Equation in Euclidean 3-Space <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">E</mi><mn>3</mn></msup></semantics></math></inline-formula>

Abstract

This work aims at investigating the geometry of surfaces corresponding to the geometry of solutions of the vortex filament equation in Euclidean 3-space E3 using the quasi-frame. In particular, we discuss some geometric properties and some characterizations of parameter curves of these surfaces in E3.

Keywords

• vortex filament equation
• Hasimoto surface
• quasi-frame
• Euclidean space