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The slant helices according to bishop frame of the spacelike curve in Lorentzian space. (English) Zbl 1190.53015

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 [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:

53B25 Local submanifolds
53B30 Local differential geometry of Lorentz metrics, indefinite metrics

Citations:

Zbl 0588.53017
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References:

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