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.


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


Zbl 0588.53017
Full Text: DOI


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