Geodesics and magnetic curves in the 4-dim almost Kähler model space \(\mathrm{F}^4\) (Q6549862)

The authors consider a four-dimensional simply connected Riemannian 3-symmetric space.\NThey study the homogeneous geometry of its model space \(F^4\) and compute its Levi-Civita connection, the Riemannian curvature, the Ricci operator, the sectional curvature and the scalar curvature.\N\NThen they introduce the notion of a symplectic pair of two Kähler forms. Some typical submanifolds of the model space \(F^4\) are studied and, in particular, some important results on geodesics and magnetic curves in the model space \(F^4\) are presented, as well as the general properties of magnetic curves with respect to the symplectic pair of Kählerian forms in an almost Kählerian 4-dimensional manifold.\N\NAs a special case the authors study the case of homogeneous geodesics and homogeneous magnetic curves in \(F^4\).