Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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BIHARMONIC CURVES IN 3-DIMENSIONAL LORENTZIAN SASAKIAN SPACE FORMS

  • Lee, Ji-Eun (Institute of Basic Science Chonnam National University)
  • Received : 2019.11.15
  • Accepted : 2020.03.23
  • Published : 2020.07.31
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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

Acknowledgement

The author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2019R1l1A1A01043457).

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