Abstract
Let ( M, g) be a complex compact hermitian manifold with dimension complex dim C = m ≥ 2, we study in this paper the critical points of the functional: Φ = 1 2 r ∫ M ¦θ¦ 2r υ g 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.
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