Deformations of balanced metrics

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 $\{ω_t\}_t$ which start with a fixed balanced metric $ω$ for $t=0$, along a differentiable family of complex manifolds $\{M_t\}_t$.

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