A note on small deformations of balanced manifolds

TL;DR

This paper proves that small deformations of compact balanced manifolds remain balanced under a weak condition, with applications to twistor spaces over self-dual four-manifolds.

Contribution

It introduces a weak condition ensuring stability of balanced structures under small deformations, extending previous results.

Findings

Small deformations preserve balanced structures under the given condition.

The condition applies to twistor spaces over compact self-dual four-manifolds.

Balanced property stability is established for a class of complex manifolds.

Abstract

In this note we prove that, under a weak condition, small deformations of a compact balanced manifold are also balanced. This condition is satisfied on the twistor space over a compact self-dual four manifold.