On some compact almost Kähler locally symmetric space.
Non-existence of almost Kähler structure on hyperbolic spaces of dimension 2n(...4).
Some critical almost Kähler structures
We consider the set of all almost Kähler structures (g,J) on a 2n-dimensional compact orientable manifold M and study a critical point of the functional with respect to the scalar curvature τ and the *-scalar curvature τ*. We show that an almost Kähler structure (J,g) is a critical point of if and only if (J,g) is a Kähler structure on M.
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