A Poisson-Kähler fibration has a canonical Kähler metric on its base whose holomorphic bisectional curvature is non-positive and whose holomorphic sectional, Ricci, and scalar curvatures are bounded above by a negative constant.
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Curvature of the base manifold of a Monge-Amp\`ere fibration and its existence
A Poisson-Kähler fibration has a canonical Kähler metric on its base whose holomorphic bisectional curvature is non-positive and whose holomorphic sectional, Ricci, and scalar curvatures are bounded above by a negative constant.