Some new results for Hasimoto surfaces
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Let σ=σ(s,t) be the position vector of a curve Γ moving on surface M in E3 such that σ=σ(s,t) is a unit speed curve for all t. If the surface M is a Hasimoto surface, then, the position vector σ satisfy the following condition
σt = σs ⋀ σss
also called as smoke ring equation or vortex filament . In that work, we investigate the geometric properties according to Bishop frame of Hasimoto surfaces in Euclidean 3-space. Also, we give some characterization of parameter curves given according to Bishop frame of Hasimoto surfaces.
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