Some critical almost Kähler structures

Volume 111 / 2008

Takashi Oguro, Kouei Sekigawa Colloquium Mathematicum 111 (2008), 205-212 MSC: 53C15, 53C55 DOI: 10.4064/cm111-2-4


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 $M$.


  • Takashi OguroDepartment of Mathematical Sciences
    School of Science and Engineering
    Tokyo Denki University
    Saitama, 350-0394, Japan
  • Kouei SekigawaDepartment of Mathematics
    Faculty of Science
    Niigata University
    Niigata, 950-2181, Japan

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