Geodesics and magnetic curves in the 4-dim almost Kähler model space F4
In: Complex Manifolds, Jg. 11 (2024), Heft 1, S. 562-564
Online
academicJournal
Zugriff:
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}.
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Geodesics and magnetic curves in the 4-dim almost Kähler model space F4
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Autor/in / Beteiligte Person: | Zlatko, Erjavec ; Jun-ichi, Inoguchi |
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Zeitschrift: | Complex Manifolds, Jg. 11 (2024), Heft 1, S. 562-564 |
Veröffentlichung: | De Gruyter, 2024 |
Medientyp: | academicJournal |
ISSN: | 2300-7443 (print) |
DOI: | 10.1515/coma-2024-0001 |
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