Abstract:
We show that a transversely oriented $C^2$-foliation of codimension one with nonnegative Ricci curvature on a closed orientable manifold is a foliation with almost no holonomy. This allows us to decompose the manifold into blocks on which this foliation has a simple structure. We also show that a manifold homeomorphic to a 5-dimensional sphere does not admit a codimension-one $C^2$-foliation with nonnegative sectional curvature.
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