Let $f : X \to Y$ be a surjective holomorphic submersion between compact Kähler manifolds. Assume the fibres are positive-dimensional. Suppose the base $Y$ and fibres $F$ admit Kähler metrics of negative (respectively, zero, or positive) Ricci curvature. Does $X$ admit a Kähler metric whose Ricci curvature has the same sign?
2026-03-27 17:35:23.1774632923
Ricci curvature of fibrations
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