A new class of non-Kähler metrics

Abstract

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

Keywords

• blow-up
• deformation
• hermitian metric
• pluriclosed
• skt
• 53c55
• 32g07
• 53c15