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Title: Topology of codimension-one foliations of nonnegative curvature. II

We prove that a 3-connected closed manifold M of dimension n≥5 does not admit a codimension-one C{sup 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{sup 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(π,1)-manifold. Bibliography: 13 titles.
Authors:
 [1]
  1. B.Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar'kov (Ukraine)
Publication Date:
OSTI Identifier:
22364684
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 10; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; MANY-DIMENSIONAL CALCULATIONS; MATHEMATICAL MANIFOLDS; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; SPHERES; TOPOLOGY