Some critical almost Kähler structures

Abstract

Abstract. 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 F λ,µ (J, g) = Ì M (λτ + µτ * ) dM g 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 F −1,1 if and only if (J, g) is a Kähler structure on M .