Bertrand mate of timelike biharmonic Legendre curves in Lorentzian Heisenberg group Heis3

Abstract

In this paper, we study Bertrand mate of timelike biharmonic Legendre curves in the Lorentzian Heisenberg group Heis3. We characterize timelike biharmonic Legendre curves in terms of their curvature and torsion. Moreover, we obtain the position vectors of timelike biharmonic Legendre curves and we construct parametric equations of Bertrand mate of timelike biharmonic Legendre curves in the Lorentzian Heisenberg group Heis3.