Balanced and strongly Gauduchon cones on solvmanifolds (Q2929938)

One of the main results of the paper under review is that if \((M,J)\) is any solvmanifold with an invariant complex structure and if there exists an invariant \((1,0)\)-form \(\alpha\neq0\) on \(M\) such that \(\alpha\wedge\bar\alpha\) is closed, then the cone of strongly Gauduchon metrics on \((M,J)\) does not contain 0. In particular, this holds for every nilmanifold endowed with an invariant complex structure. In the final section of the paper, the cones of balanced metrics and of strongly Gauduchon metrics are described for any invariant complex structure on a certain 6-dimensional nilmanifold.