Local rigidity of certain classes of almost Kahler 4-manifolds

Abstract

We show that any non-Kahler, almost Kahler 4-manifold for which both the Ricci and the Weyl curvatures have the same algebraic symmetries as they have for a Kahler metric is locally isometric to the (only) proper 3-symmetric 4-dimensional space described by O. Kowalski.

LaTex file, 25 pages, typos corrected, improved presentation, accepted in Ann. Global Anal. Geom