• 대한수학회논문집
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• 제33권4호
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• pp.1309-1320
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• 2018

In this paper, we show that proper biharmonic spacelike curve ${\gamma}$ in Lorentzian Heisenberg space (${\mathbb{H}}_3$, g) is pseudo-helix with ${\kappa}^2-{\tau}^2=-1+4{\eta}(B)^2$. Moreover, ${\gamma}$ has the spacelike normal vector field and is a slant curve. Finally, we find the parametric equations of them.

• 대한수학회논문집
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• 제35권3호
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• pp.967-977
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• 2020

In this article, we find the necessary and sufficient condition for a proper biharmonic Frenet curve in the Lorentzian Sasakian space forms 𝓜³₁(H) except the case constant curvature -1. Next, we find that for a slant curve in a 3-dimensional Sasakian Lorentzian manifold, its ratio of "geodesic curvature" and "geodesic torsion -1" is a constant. We show that a proper biharmonic Frenet curve is a slant pseudo-helix with 𝜅² - 𝜏² = -1 + 𝜀₁(H + 1)𝜂(B)² in the Lorentzian Sasakian space forms x1D4DC³₁(H) except the case constant curvature -1. As example, we classify proper biharmonic Frenet curves in 3-dimensional Lorentzian Heisenberg space, that is a slant pseudo-helix.