Parallel surfaces of the non-lightlike solution of vortex filament equations
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Melek Erdoğdu
Abstract
In this paper, we investigate the parallel surfaces of the nonlightlike solution of vortex filament equations, namely, the parallel surfaces to Hasimoto surfaces in
Communicated by Tibor Macko
References
[1] Abdelaziz, H. S.—Khalifa, M.—Kiziltuğ, S.: Parallel surfaces of Weingarten type in Minkowski 3-space, Int. Math. Forum 7 (2012), 2293–2302.Search in Google Scholar
[2] Ding, Q.—Inoguchi, J.: Schrödinger flows, binormal motion for curves and second AKNS-hierarchies, Chaos Solitons Fractals 21 (2004), 669–677.10.1016/j.chaos.2003.12.092Search in Google Scholar
[3] Erdoğdu, M.—Özdemir, M.: Geometry of Hasimoto surfaces in Minkowski 3-space, Math. Phys. Anal. Geom. 17 (2014), 169–181.10.1007/s11040-014-9148-3Search in Google Scholar
[4] Görgülü, A.—Çöken, A. C.: The dupin indicatrix for parallel pseudo-Euclidean hypersurfaces in pseudo-Euclidean space in semi-Euclidean space
[5] Gürbüz, N.: The motion of timelike surfaces in timelike geodesic coordinates, Int. J. Math. Anal. 4 (2010), 349–356.Search in Google Scholar
[6] Hasimoto, H.: A soliton on a vortex filament, J. Fluid Mech. 51 (1972), 477–485.10.1017/S0022112072002307Search in Google Scholar
[7] Inoguchi, J.: Timelike surfaces of constant mean curvature in Minkowski 3-space, Tokyo J. Math. 21 (1998), 141–152.10.3836/tjm/1270041992Search in Google Scholar
[8] Inoguchi, J.: Biharmonic curves in Minkowski 3-space, Int. J. Math. Math. Sci. 41 (2003), 1365–1368.10.1155/S016117120320805XSearch in Google Scholar
[9] Lopez, R.: Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int. Electron. J. Geom. 7 (2014), 44–107.10.36890/iejg.594497Search in Google Scholar
[10] Özdemir, M.—Ergin, A. A.: Rotations with unit timelike quaternions in Minkowski 3-space, J. Geom. Phys. 56 (2006), 322–336.10.1016/j.geomphys.2005.02.004Search in Google Scholar
[11] Özdemir, M.—Ergin, A. A.: Parallel frames of non-lightlike curves, Missouri J. Math. Sci. 20 (2008), 127–137.10.35834/mjms/1316032813Search in Google Scholar
[12] Rogers, C.—Schief, W. K.: Bäcklund and Darboux Transformations, Geometry and Modern Applications in Soliton Theory, Cambridge University Press, United Kingdom, 2002.10.1017/CBO9780511606359Search in Google Scholar
[13] Schief, W. K.—Rogers, C.: Binormal motion of curves of constant curvature and torsion. Generation of soliton surfaces, Proc. R. Soc. Lond. Ser. A 455 (1988), 3163–3188.10.1098/rspa.1999.0445Search in Google Scholar
[14] Ünlütürk, Y. —Özüsağlam, E.: On parallel surfaces in Minkowski 3-space, TWMS J. App. Eng. Math. 3 (2013), 214–222.Search in Google Scholar
[15] Yayli, Y.—Sağlam, D.—Kalkan, Ö.: Parallel linear Weingarten surfaces in 피3 and
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Articles in the same Issue
- On the Paley graph of a quadratic character
- A topological duality for tense modal pseudocomplemented De Morgan algebras
- Fibonacci numbers as mixed concatenations of Fibonacci and Lucas numbers
- A general formula in composition theory
- A nonlinear Filbert-like matrix with three free parameters: From linearity to nonlinearity
- On universality in short intervals for zeta-functions of certain cusp forms
- On asymptotics for lacunary partition functions
- Parallel surfaces of the non-lightlike solution of vortex filament equations
- New q-analogues of Van Hamme’s (F.2) supercongruence and of some related supercongruences
- Kneser-type oscillation theorems for second-order functional differential equations with unbounded neutral coefficients
- Approximation theorems via Pp-statistical convergence on weighted spaces
- Global existence and multiplicity of positive solutions for anisotropic eigenvalue problems
- Theoretical analysis of higher-order system of difference equations with generalized balancing numbers
- On a solvable difference equations system of second order its solutions are related to a generalized Mersenne sequence
- Positive bases, cones, Helly-type theorems
- Digital Jordan surfaces arising from tetrahedral tiling
- Influence of ideals in compactifications
- On the functions ωf and Ωf
- On the 𝓐-generators of the polynomial algebra as a module over the Steenrod algebra, I
- A bivariate distribution with generalized exponential conditionals
- A note on boundary feedback stabilization for degenerate parabolic equations in multi-dimensional domains
