An almost Kähler Cheeger--Gromoll splitting theorem with applications

In this paper, we establish an almost Kähler analogue of the Cheeger–Gromoll splitting theorem for complete almost Kähler manifolds with nonnegative Ricci curvature. As applications, we use the splitting to obtain Goldberg-type integrability results and establish a relation between symplectic non-hyperbolicity and nonnegative Ricci curvature via a theorem of Bangert.