On a compact locally conformal K & auml;hler manifold (which is also Gauduchon) satisfying an Einstein-type condition, an inequality between the integrations of Chern forms and the Bochner curvature tensor is proved. While on a compact Gauduchon surface, two similar inequalities are derived.
We revisit the second order estimate for solutions to the quaternionic Calabi-Yau problem on hyperkähler manifolds, originally established by Dinew and Sroka. In this note, we present a simplified argument to derive the estimate.
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.
In this article, we introduce certain arity-3 operations on complex manifolds arising from homotopy transfer theory. Such operations are related to the triple ABCABC-Massey products from Bott-Chern to Aeppli cohomology. We present a package for computing such products as well as other cohomological and homotopical invariants for complex nilmanifolds and give some examples.
We survey some results and open questions related to various algebraic invariants of compact complex manifolds that can be obtained from differential forms.
