Deformations of balanced metrics

Abstract

Small deformations of the complex structure do not always preserve special metric properties in the Hermitian non-Kähler setting. In this paper, we find necessary conditions for the existence of smooth curves of balanced metrics $\{{\omega }_t{\}}_t$ which start with a fixed balanced metric $\omega$ for $t=0$, along a differentiable family of complex manifolds $\{M_t{\}}_t$.

arXiv comment15 pages. arXiv admin note: text overlap with arXiv:2008.11983