Binormal Motion of Curves with Constant Torsion in 3-Spaces

Arroyo, J.; Garay, Óscar J.; Pámpano, Álvaro

doi:10.1155/2017/7075831

Cited by 27 publications

(35 citation statements)

References 10 publications

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“…κ being the curvature of γ in B(ρ) and G(s) = y t , y t 1/2 (for details see [4]). Now, after long, straightforward computations, one can see that the Gauss and Weingarten formulae lead to a PDE system to be satisfied by y (see, for instance, [4]).…”

Section: Correspondence Resultsmentioning

confidence: 99%

Critical tori for mean curvature energies in Killing submersions

Pámpano

2020

Nonlinear Analysis

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We study surface energies depending on the mean curvature in total spaces of Killing submersions, which extend the classical notion of Willmore energy. Based on a symmetry reduction procedure, we construct vertical tori critical for these mean curvature energies. These vertical tori are based on closed curves critical for curvature energy functionals in Riemannian 2-space forms.The binormal evolution of these critical curves in Riemannian 3-space forms generates rotational tori solutions for an ample family of Weingarten surfaces. Therefore, we also introduce some correspondence results between these two types of tori and illustrate their relation.

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Section: Correspondence Resultsmentioning

confidence: 99%

Critical tori for mean curvature energies in Killing submersions

Pámpano

2020

Nonlinear Analysis

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“…Barros et al computed soliton solutions of the Betchov-Da Rios equation explicitly in the anti-De Sitter and Lorentzian space forms [28,29] . Arroyo studied binormal flow with torsion and curvature to investigate the evolution of filaments [30] .…”

Section: Introductionmentioning

confidence: 99%

Fractional solutions for the inextensible Heisenberg antiferromagnetic fow and solitonic magnetic flux surfaces in the binormal direction

Körpınar

Demi̇rkol²,

Körpınar

et al. 2021

Rev. Mex. Fís.

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Motivated by recent researches in magnetic curves and their flows in different types of geometric manifolds and physical spacetime structures, we compute Lorentz force equations associated with the magnetic b-lines in the binormal direction. Evolution equations of magnetic b-lines due to inextensible Heisenberg antiferromagnetic flow are computed to construct the soliton surface associated with the inextensible Heisenberg antiferromagnetic flow. Then, their explicit solutions are investigated in terms of magnetic and geometric quantities via the conformable fractional derivative method. By considering arc-length and time-dependent orthogonal curvilinear coordinates, we finally determine the necessary and sufficient conditions that have to be satisfied by these quantities to define the Lorentz magnetic flux surfaces based on the inextensible Heisenberg antiferromagnetic flow model.

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“…In [5] we studied CMC surfaces in Riemannian and Lorentzian 3-space forms, M 3 r (ρ), which are invariant under the flow of a Killing vector field of the ambient space. We described any CMC invariant surface locally as a binormal evolution surface [4], [10]. As a consequence, they are warped product surfaces whose warping functions are solutions of an Ermakov-Milne-Pinney equation with constant coefficients.…”

Section: Introductionmentioning

confidence: 99%