Geometry of Hasimoto surfaces in Minkowski 3-space. (English) Zbl 1299.53008
Summary: In this paper, we investigate the Hasimoto surfaces in Minkowski 3-space. We discussed the geometric properties of Hasimoto surfaces in \(\mathbb M^3\) for three cases. The Gaussian and mean curvature of Hasimoto surface are found for each case. Then, we give the characterization of parameter curves of Hasimoto surfaces in \(\mathbb M^3\).
MSC:
| 53A05 | Surfaces in Euclidean and related spaces |
| 53B30 | Local differential geometry of Lorentz metrics, indefinite metrics |
References:
| [1] | Fujika, A., Inoguchi, J.: Spacelike surfaces with harmonic inverse mean curvature. J. Math. Sci. Univ. Tokyo 7, 657-698 (2000) · Zbl 1018.53007 |
| [2] | Gürbüz, N.: Intrinstic Geometry of NLS Equation and Heat System in 3- Dimensional Minkowski Space. Adv. Stud. Theor. 4, 557-564 (2010) · Zbl 1218.83005 |
| [3] | Gürbüz, N.: The Motion of Timelike Surfaces in Timelike Geodesic Coordinates. Int. J. Math. Anal. 4 (2010) · Zbl 1241.53011 |
| [4] | Hasimoto, H.: A Soliton on a vortex filament. J. Fluid. Mech. 51, 477-485 (1972) · Zbl 0237.76010 · doi:10.1017/S0022112072002307 |
| [5] | Inoguchi, J.: Timelike surfaces of constant mean curvaturein Minkowski 3-space. Tokyo J. Math. 21, 141-152 (1998) · Zbl 0930.53042 · doi:10.3836/tjm/1270041992 |
| [6] | Inoguchi, J.: Biharmonic curves in Minkowski 3-space. Int. J. Matehmatics Math. Sci. 21, 1365-1368 (2003) · Zbl 1076.53501 · doi:10.1155/S016117120320805X |
| [7] | Özdemir, M., Ergin, A.A.: Rotations with unit timelike quaternions in Minkowski 3-space. J. Geom. Phys. 56, 322-336 (2006) · Zbl 1088.53010 · doi:10.1016/j.geomphys.2005.02.004 |
| [8] | Özdemir, M., Ergin, A.A.: Parallel Frames of Non-Lightlike Curves. Missouri J. Math. Sci. 20, 127-137 (2008) · Zbl 1145.53301 |
| [9] | Rogers, C., Schief, W. K.: Intrinsic geometry of the NLS equation and its backlund transformation. Stud. Appl. Math. 101, 267-288 (1998) · Zbl 1020.35100 · doi:10.1111/1467-9590.00093 |
| [10] | Rogers, C., Schief, W.K.: Backlund and Darboux Transformations, Geometry of Modern Applications in Soliton Theory. Cambridge University Press (2002) · Zbl 1019.53002 |
| [11] | Schief, W.K., Rogers, C.: Binormal Motion of Curves of Constant Curvature and Torsion. Generation of Soliton Surfaces. Proc. R. Soc. Lond. A 455, 3163-3188 (1999) · Zbl 0981.53061 · doi:10.1098/rspa.1999.0445 |
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