A note on almost Kähler and nearly Kähler submersions
Let \((M,g,J)\) and \((B,g',J')\) be almost Hermitian manifolds. A Riemannian submersion \(\pi:M\to B\) is called an almost Hermitian submersion if \(\pi_*J= J'\pi_*\). An almost Hermitian submersion is called a nearly Kähler or an almost Kähler submersion if the total space is nearly Kähler or almost Kähler, respectively. The aim of this paper is to study the curvature of the total space, of the fibres and of the base manifold of such submersions. Further, the authors prove: If \(\pi\) is a nearly Kähler (almost Kähler) submersion, then the horizontal distribution of \(\pi\) is integrable and totally geodesic.
scientific article; zbMATH DE number 1565895