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Topology of codimension-one foliations of nonnegative curvature. II

机译:非负曲率的余维一叶的拓扑。 II

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We prove that a 3-connected(1) closed manifold M of dimension n >= 5 does not admit a codimension-one C-2-foliation of nonnegative curvature. In particular, this gives a complete answer to a question of Stuck on the existence of codimension-one foliations of nonnegative curvature on spheres. We also consider codimension-one C-2-foliations of nonnegative Ricci curvature on a closed manifold M with leaves having finitely generated fundamental group, and show that such a foliation is flat if and only if M is a K(pi, 1)-manifold.
机译:我们证明尺寸为n> = 5的3连通(1)闭合歧管M不允许非负曲率的余维一C-2-叶面。特别是,这完全解决了Stuck关于球体上存在非负曲率的余维一叶的问题。我们还考虑了闭合歧管M上非负Ricci曲率的余维一C-2-叶片,其中叶具有有限生成的基团,并且证明只有当M为K(pi,1)-时,这种叶片才是平坦的。流形。

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