Biharmonic curves in 3-dimensional Lorentzian Sasakian space forms
Commun. Korean Math. Soc.
Published online May 21, 2020
Ji-Eun Lee
Chonnam National University
Abstract : In this article,
we find the necessary and sufficient condition for a proper biharmonic Frenet curve in the Lorentzian Sasakian space forms $\mathcal{M}_1^3 (H)$ except the case constant curvature $-1$.
Next,
we find that for a slant curve in a $3$-dimensional Sasakian Lornetzian 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 $\kappa^2-\tau^2=-1+\varepsilon_1(H+1)\eta(B)^2$ in the Lorentzian Sasakian space forms $\mathcal{M}_1^3 (H)$ 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.
Keywords : Slant curves, Legendre curves, biharmonic, Lorentzian Sasakian space forms
MSC numbers : 53C25, 53C50
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