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We firstly characterize uniformly quasi accelerated motion (UQAM) with Fermi Walker derivation. We obtain new energy of quasi tangent magnetic biharmonic particle and Lorentz field. Thus, we give new relationship between Fermi Walker parallelism and uniformly quasi accelerated motion in Heisenberg group. Moreover, we give applied geometric characterization for a uniformly quasi accelerated motion of velocity magnetic biharmonic particles in Heisenberg space. © 2022 King Saud University, KSU Researchers Supporting Project number (RSP2021/158), King Saud University, Riyadh, Saudi Arabia.

In this paper, we firstly review the quasi uniformly accelerated motion (QUAM) with Fermi derivative by cold plasma in Heisenberg space. We define new quasi uniformly accelerated potential electric energy of quasi normal magnetic biharmonic particles and some Lorentz fields. Moreover, we design the new relationship between the quasi uniformly accelerated motion and the Fermi parallel transportation in cold plasma. Also, we collect new physical geometric designs for a quasi uniformly accelerated motion of normal magnetic biharmonic particles in Heisenberg space. Finally, we construct quasi uniformly accelerated potential electric energy with respect to its electric field and some quasi curvatures. © 2022. All Rights Reserved. The authors would like to express their sincere gratitude to the referees for the valuable suggestions to improve the paper.

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 paper, we firstly review the optical circular motion with optical optimistic density in Heisenberg space. We define new quasi optical potential electromagnetic energy of quasi normal magnetic biharmonic fields. Moreover, we design the new characterization of uniformly optical electroosmotic phase and optical parallel transportation in cold plasma. Also, we collect new physical geometric designs for a optical optimistic density of normal magnetic biharmonic fields in Heisenberg space. Finally, we construct optical potential electromagnetic energy with respect to its electric field and sonic crystals.

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.

In the present article, we define a new concept of normal magnetic particles by using biharmonic particles in Heisenberg space. We characterize the energy of normal magnetic particles and some Lorentz fields. Furthermore, we show that energy and magnetic flux density can be stated by Frenet fields in Heisenberg space.

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