A new class of non-Kähler metrics

We study the stability at blow-ups and deformations of a class of Hermitian metrics whose fundamental two-form ω ω satisfies the condition ∂ ∂ ¯ ω k = 0 ∂ ∂ ̄{ω }ᵏ=0 , for any k k between 1 and n − 1 n-1 (where n n is the complex dimension of the manifold). We are motivated by the existence of compact complex manifolds supporting such metrics.