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http://dx.doi.org/10.4134/CKMS.c190393

BIHARMONIC CURVES IN 3-DIMENSIONAL LORENTZIAN SASAKIAN SPACE FORMS  

Lee, Ji-Eun (Institute of Basic Science Chonnam National University)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.3, 2020 , pp. 967-977 More about this Journal
Abstract
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.
Keywords
Slant curves; Legendre curves; biharmonic; Lorentzian Sasakian space forms;
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Times Cited By KSCI : 3  (Citation Analysis)
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