Geodesics and magnetic curves in the 4-dim almost Kähler model space F4

Abstract

We study geodesics and magnetic trajectories in the model space F4{{\rm{F}}}^{4}. The space F4{{\rm{F}}}^{4} is isometric to the 4-dim simply connected Riemannian 3-symmetric space due to Kowalski. We describe the solvable Lie group model of F4{{\rm{F}}}^{4} and investigate its curvature properties. We introduce the symplectic pair of two Kähler forms on F4{{\rm{F}}}^{4}. Those symplectic forms induce invariant Kähler structure and invariant strictly almost Kähler structure on F4{{\rm{F}}}^{4}. We explore some typical submanifolds of F4{{\rm{F}}}^{4}. Next, we explore the general properties of magnetic trajectories in an almost Kähler 4-manifold and characterize Kähler magnetic curves with respect to the symplectic pair of Kähler forms. Finally, we study homogeneous geodesics and homogeneous magnetic curves in F4{{\rm{F}}}^{4}.

Keywords

• 4-dim thurston space
• almost kähler 3-symmetric space f4
• geodesics
• magnetic trajectories
• 53c15
• 53c30
• 53c55
• 53c80