Biharmonic spacelike curves in Lorentzian Heisenberg space

Ji-Eun Lee

doi:10.4134/CKMS.c170376

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2018; 33(4): 1309-1320

Online first article April 10, 2018 Printed October 31, 2018

https://doi.org/10.4134/CKMS.c170376

Biharmonic spacelike curves in Lorentzian Heisenberg space

Ji-Eun Lee

Chonnam National University

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Abstract

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

Keywords: slant curves, biharmonic curves, Lorentzian Heisenberg space

MSC numbers: Primary 53B25, 53C25