In this paper, we describe a new method for constructing a canal surface surrounding a timelike horizontal biharmonic curve in the Lorentzian Heisenberg group Heis 3 . Firstly, we characterize timelike biharmonic curves in terms of their curvature and torsion. Also, by using timelike horizontal biharmonic curves, we give explicit parametrizations of canal surfaces in the Lorentzian Heisenberg group Heis 3 .
In this paper, we study tangent surfaces of biharmonic B-general helices according to Bishop frame in the Heisenberg group Heis 3. We give necessary and sufficient conditions for B-general helices to be biharmonic according to Bishop frame. We characterize the tangent surfaces of biharmonic B-general helices in terms of Bishop frame in the Heisenberg group Heis 3. Additionally, we illustrate our main theorem.
In this paper, we study energy of time-like horizontal biharmonic curves in the Lorentzian Heisenberg group Heis3. We characterize the biharmonic curves in terms of their curvature and torsion. We prove that all of the biharmonic curves are helices. Finally, we study the mechanics of biharmonic curves and provide conditions for energy of horizontal biharmonic curves
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