On the Kähler-likeness on almost Hermitian manifolds

Abstract

We define a Kähler-like almost Hermitian metric. We will prove that on a compact Kähler-like almost Hermitian manifold (M2n, J, g), if it admits a positive ∂ ̄∂-closed (n − 2, n − 2)-form, then g is a quasi-Kähler metric.

Keywords

• almost hermitian manifolds
• kähler-like metrics
• chern connection
• quasi-kähler metrics
• 53c15 (primary)
• 53c55 (secondary)