Variation de la L2r-norme de la 1-forme de torsion sur une variété hermitienne compacte

AbstractLet (M,g) be a complex compact hermitian manifold with dimension complex dimC = m ≥ 2, we study in this paper the critical points of the functional: Φ = 12r ∫M ¦θ¦2r υg in the set of the hermitian metrics with total volume equal to one, where θ is 1 — form of torsion of the Chern connexion and r is a real number such that 1 ≤ r ≤ m. We show that the critical points of this functional are exactly a semi-kählerian metric