Some critical almost Kähler structures

Takashi Oguro¹ ; Kouei Sekigawa²

¹ Department of Mathematical Sciences School of Science and Engineering Tokyo Denki University Saitama, 350-0394, Japan
² Department of Mathematics Faculty of Science Niigata University Niigata, 950-2181, Japan

Colloquium Mathematicum, Tome 111 (2008) no. 2, pp. 205-212

Résumé

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 $M$.

Détail

DOI : 10.4064/cm111-2-4

Keywords: consider set almost hler structures n dimensional compact orientable manifold study critical point functional scr lambda int lambda tau tau * respect scalar curvature tau * scalar curvature tau * almost hler structure critical point scr only hler structure nbsp