Position vector of spacelike biharmonic curves in the Lorentzian Heisenberg group Heis 3
In this paper, we study spacelike biharmonic curves in the Lorentzian Heisenberg group Heis 3 . We show that spacelike biharmonic curves are general helices. We characterize position vector of spacelike biharmonic general helices in terms of their curvature and torsion.
Biharmonic submanifolds in 3-dimensional (κ, μ)-manifolds
Biharmonic maps between Riemannian manifolds are defined as critical points of the bienergy and generalized harmonic maps. In this paper, we give necessary and sufficient conditions for nonharmonic Legendre curves and anti-invariant surfaces of 3-dimensional (κ,μ)-manifolds to be biharmonic.
Position Vectors of Spacelike Biharmonic Horizontal Curves with Spacelike Binormal in Lorenzian Heisenberg Group Heis 3
In this paper, we show that every spacelike biharmonic curve in the Lorentzian Heisenberg group Heis 3 is a helix (both of whose curvature and torsion are constants). We give some characterizations for spacelike biharmonic curve by using the positions vectors of the curve.