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Zbl 1190.53015
Bukcu, Bahaddin; Karacan, Murat Kemal
The slant helices according to bishop frame of the spacelike curve in Lorentzian space. (English)
[J] J. Interdiscip. Math. 12, No. 5, 691-700 (2009). ISSN 0972-0502; ISSN 2169-012X/e

T. Ikawa obtained the following differential equation $$D_TD_TD_TT-KD_TT, \quad K = \kappa^2-\tau^2$$ for the circular helix which corresponds the case when the curvature $\kappa$ and torsion $\tau$ of space-like curve with a space-like binormal $\alpha$ on the Lorentzian manifold $M_1$ are constant [{\it T. Ikawa}, Tsukuba J. Math. 9, 353--371 (1985; Zbl 0588.53017)]. In this paper, we define a slant helix with the help of the Bishop frame of the space-like curve with a space-like binormal. Furthermore, we give some necessary and sufficient conditions for the slant helix and T. Ikawa's result is generalized to the case of the general slant helix.

MSC 2000:: *53B25 Local submanifolds
53B30 Lorentz metrics, indefinite metrics

Keywords: slant helix; Bishop frame; parallel adapted frame; space-like curve; Lorentzian space

Citations: Zbl 0588.53017

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