Abstract
We consider various types of special Hermitian metrics on compact complex manifolds, namely Kahler, Hermitian-symplectic, SKT, balanced and strongly Gauduchon metrics. We study the strongly Gauduchon metrics in relation to the SKT condition on complex nilmanifolds and to the Hermitian-symplectic condition on certain complex solvmanifolds. We also review the behaviour of the existence properties of these special metrics on compact complex manifolds under holomorphic deformations.
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