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In the present paper, we firstly discuss the normal biharmonic magnetic particles in the Heisenberg space. We express new uniform motions and its properties in the Heisenberg space. Moreover, we obtain a new uniform motion of Fermi&ndash, Walker derivative of normal magnetic biharmonic particles in the Heisenberg space. Finally, we investigate uniformly accelerated motion (UAM), the unchanged direction motion (UDM), and the uniformly circular motion (UCM) of the moving normal magnetic biharmonic particles in Heisenberg space.

In this study, we investigate new type of normal magnetic force biharmonic particles associated with a magnetic field $$\mathcal {B}$$ defined on Heisenberg space. Firstly, we consider a moving charged biharmonic particle under the action of a normal force $$\mathbf {N}$$ in the magnetic field $$\mathcal {B}.~$$ Then, we assume that trajectories of the particle associated with the magnetic field $$\mathcal {B}$$ correspond to normal magnetic force ( $$\mathbf {N}_{\mathbf {f}}$$ ) biharmonic particles of magnetic vector field $$\mathcal {B}$$ on 3D Heisenberg space.

In this work, we consider velocity bimagnetic biharmonic particle on 3D Heisenberg space in the magnetic field B and we give the concept of energy. Moreover, we characterize energy conditions of velocity bimagnetic biharmonic particles with Frenet vector field. Therefore, we obtain energy results for bimagnetic particles by Frenet fields in the Heisenberg space. © 2018, Universidad Catolica del Norte.

We construct most symmetric Saddle towers in Heisenberg space i.e. periodic minimal surfaces that can be seen as the desingularization of vertical planes intersecting equiangularly. The key point is the construction of a suitable barrier to ensure the convergence of a family of bounded minimal disks. Such a barrier is actually a periodic deformation of a minimal plane with prescribed asymptotic behavior. A consequence of the barrier construction is that the number of disjoint minimal graphs suppoerted on domains is not bounded in Heisenberg space., Comment: 20 pages. V2: addition of a result. V3: minor corrections

We give an immersion formula, the Sym-Bobenko formula, for minimal surfaces in the 3-dimensional Heisenberg space. Such a formula can be used to give a generalized Weierstrass type representation and construct explicit examples of minimal surfaces., 5 pages