Slant helices: a new approximation
Slant helices: a new approximation
In this paper, we study a weaker version of classic slant helices in Euclidean space $R^3$ or Minkowski space $R_1^3$, which will be called general slant helices. We show that any classic slant helix is a general slant helix but the converseis not true. We also obtain equations involving the curvature and torsion that characterize this family of curves
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- [1] Ali AT, López R. Slant helices in Minkowski space E31
. J Korean Math Soc 2011; 48: 159-167.
- [2] Barros M. General helices and a theorem of Lancret. P Am Math Soc 1997; 125: 1503-1509.
- [3] Barros M, Ferrández A, Lucas P, Meroño MA. General helices in the 3-dimensional Lorentzian space forms. Rocky
Mt J Math 2001; 31: 373-388.
- [4] Ferrández A, Giménez A, Lucas P. s-Degenerate curves in Lorentzian space forms. J Geom Phys 2003; 45: 116-129.
- [5] Giménez A. Relativistic particles along null curves in 3D Lorentzian space forms. Int J Bifurcat Chaos 2010; 20:
2851-2859.
- [6] Huang R, Liao C. Geometrical particle models on 3D lightlike curves. Mod Phys Lett A: 2006; 21: 3039-3048.
- [7] Izumiya S, Takeuchi N. New special curves and developable surfaces. Turk J Math 2004; 28: 153-163.
- [8] Langer J, Singer DA. The total squared curvature of closed curves. J Differ Geom 1984; 20: 1-22.
- [9] López R. Differential geometry of curves and surfaces in Lorentz-Minkowski space. Int Electron J Geom 2014; 7:
44-107.
- [10] Lucas P, Ortega-Yagües JA. Slant helices in the three-dimensional sphere. J Korean Math Soc 2017; 54: 1331-1343.
- [11] Lucas P, Ortega-Yagües JA. Helix surfaces and slant helices in the three-dimensional anti-De Sitter space. RACSAM
Rev R Acad A 2017; 11: 1201-1222.
- [12] Mira P, Pastor JA. Helicoidal maximal surfaces in Lorentz-Minkowski space. Monatsh Math 2003; 140: 315-334.
- [13] Salkowski E. Zur Transformation von Raumkurven. Math Ann 1909; 66: 517-557.
- [14] Walrave J. Curves and surfaces in Minkowski space. PhD, Katholieke Universiteit Leuven, Leuven, Belgium, 1995.