Compact quotients of real semisimple Lie groups with regular complex structures admit balanced or pluriclosed metrics according to Vogan diagrams but never both, with a corrected classification of the structures.
Complex parallisable manifolds.Proc
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Balanced and pluriclosed metrics on real semisimple Lie groups
Compact quotients of real semisimple Lie groups with regular complex structures admit balanced or pluriclosed metrics according to Vogan diagrams but never both, with a corrected classification of the structures.