Dynamics on \(\mathbb{S}^3\) and the Hopf fibration

DOI10.1016/j.amc.2018.11.027zbMath1428.53037OpenAlexW2902096462MaRDI QIDQ2008524

Ana Irina Nistor, Marian Ioan Munteanu, Osman Ateş

Publication date: 26 November 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2018.11.027

zbMATH Keywords

Hopf mapLegendre curvemagnetic curveHopf tube\(J\)-trajectory

Mathematics Subject Classification ID

Dynamics induced by flows and semiflows (37C10) Applications of global differential geometry to the sciences (53C80) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Geodesics in global differential geometry (53C22) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Curves in Euclidean and related spaces (53A04)

Related Items (2)

\(J\)-trajectories in 4-dimensional solvable Lie group \(\mathrm{Sol}_0^4\) ⋮ \(J\)-trajectories in 4-dimensional solvable Lie group \(\mathrm{Sol}_1^4\)

Uses Software

• Mathematica
• CandS

Cites Work

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• Log-aesthetic curves as similarity geometric analogue of Euler's elasticae
• Periodic \(J\)-trajectories on \(\mathbb{R} \times \mathbb{S}^3\)
• Deformable flat tori in \(S^3\) with constant mean curvature
• The Hopf fibration --- seven times in physics
• Periodic magnetic curves in Berger spheres
• Constant angle surfaces in Lorentzian Berger spheres
• Magnetic vortex filament flows
• The contact magnetic flow in 3D Sasakian manifolds
• BÄCKLUND TRANSFORMATIONS AND KNOTS OF CONSTANT TORSION
• Explicit Characterization of Spherical Curves
• On an Explicit Characterization of Spherical Curves

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