Geometry of curve flows in isotropic spaces

DOI10.3934/math.2020222zbMath1484.53015OpenAlexW3014803952MaRDI QIDQ2129967

Nevin Gürbüz, Dae Won Yoon

Publication date: 25 April 2022

Published in: AIMS Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/math.2020222

zbMATH Keywords

Hasimoto surfaceSchrödinger flowisotropic spaceextended Harry-Dym flow

Mathematics Subject Classification ID

Global submanifolds (53C40) Curves in Euclidean and related spaces (53A04) Non-Euclidean differential geometry (53A35) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (2)

Hasimoto maps for nonlinear Schrödinger equations in Minkowski space ⋮ Vortex filament flows for curves in a 3-dimensional pseudo-Riemannian manifold

Cites Work

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• Translation surfaces of constant curvatures in a simply isotropic space
• Generated surfaces via inextensible flows of curves in \(\mathbb R^3\)
• On new characterization of inextensible flows of space-like curves in de Sitter space
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• Binormal motion of curves with constant torsion in 3-spaces
• Bäcklund transformations for integrable geometric curve flows
• The Korteweg–de Vries hierarchy as dynamics of closed curves in the plane
• Binormal motion of curves of constant curvature and torsion. Generation of soliton surfaces
• A soliton on a vortex filament

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