Negatively curved homogeneous almost Kahler Einstein manifolds with nonpositive curvature operator

Given a homogeneous almost Kahler manifold (M, J, g) with nonpositive curvature operator, we prove that if g is an Einstein metric having negative sectional curvature, then the almost complex structure J must be integrable. Furthermore, such (M, J, g) eventually has constant negative holomorphic sectional curvature and hence is holomorphically isometric to a complex hyperbolic space.