Non-negative Ricci curvature on one leaf of the Koszul foliation forces a Hessian metric to be flat and bounds the first Betti number by dimension and leaf topology.
On the topology of complete manifolds of non-negative ricci curvature
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Ricci Curvature and Betti Numbers of Hessian Manifolds
Non-negative Ricci curvature on one leaf of the Koszul foliation forces a Hessian metric to be flat and bounds the first Betti number by dimension and leaf topology.