Deformations of Strong K\"ahler with torsion metrics

TL;DR

This paper investigates the stability of strong K"ahler with torsion (SKT) metrics under small deformations, establishing necessary conditions for their persistence in families of complex manifolds.

Contribution

It provides new necessary conditions for the stability of SKT metrics under deformations, addressing a previously known instability issue.

Findings

Identifies conditions under which SKT metrics remain stable during deformations

Shows that SKT stability is not guaranteed under small perturbations

Advances understanding of the deformation theory of SKT structures

Abstract

Existence of strong K\"ahler with torsion metrics, shortly SKT metrics, on complex manifolds has been shown to be unstable under small deformations. We find necessary conditions under which the property of being SKT is stable for a smooth curve of Hermitian metrics $\{\omega_t\}_t$ which equals a fixed SKT metric $\omega$ for $t=0$, along a differentiable family of complex manifolds $\{M_t\}_t$.