Geodesics and magnetic curves in the 4-dim almost Kähler model space F<sup>4</sup>-Reference-Cited by-同舟云学术

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

Published:2024-01-01 Issue:1 Volume:11 Page:
ISSN:2300-7443
Container-title:Complex Manifolds
language:en
Short-container-title:

Author:

Erjavec Zlatko¹^ORCID,Inoguchi Jun-ichi²^ORCID

Affiliation:

1. Faculty of Organization and Informatics , University of Zagreb , HR-42000 , Varaždin , Croatia

2. Department of Mathematics , Hokkaido University , Sapporo 060-0810 , Japan

Abstract

Abstract We study geodesics and magnetic trajectories in the model space

F 4

{{\rm{F}}}^{4}

. The space

F 4

{{\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

F 4

{{\rm{F}}}^{4}

and investigate its curvature properties. We introduce the symplectic pair of two Kähler forms on

F 4

{{\rm{F}}}^{4}

. Those symplectic forms induce invariant Kähler structure and invariant strictly almost Kähler structure on

F 4

{{\rm{F}}}^{4}

. We explore some typical submanifolds of

F 4

{{\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

F 4

{{\rm{F}}}^{4}

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/coma-2024-0001/pdf

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