Some critical almost Kähler structures
Volume 111 / 2008
Colloquium Mathematicum 111 (2008), 205-212
MSC: 53C15, 53C55
DOI: 10.4064/cm111-2-4
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 ${\scr F}_{\lambda,\mu}(J,g) = \int_M (\lambda \tau + \mu \tau^*)\, dM_g$ with respect to the scalar curvature $\tau$ and the $*$-scalar curvature $\tau^*$. We show that an almost Kähler structure $(J,g)$ is a critical point of ${\scr F}_{-1,1}$ if and only if $(J,g)$ is a Kähler structure on $M$.
