Examples of compact non-Kähler almost Kähler manifolds

Abstract

A parametrized family of compact non-Kähler almost Kähler manifolds M 2 r + 2 {M^{2r + 2}} , r ⩾ 1 r \geqslant 1 , is constructed. For r r odd, these manifolds are shown to have odd first Betti number, so they cannot be Kählerian.