Geodesic
Topology of codimension-one foliations of nonnegative curvature.~II
Sbornik. Mathematics, Tome 205 (2014) no. 10, pp. 1373-1386

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We prove that a 3-connected closed manifold $M$ of dimension $n\geqslant 5$ 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. Bibliography: 13 titles.
Keywords: Riemannian manifold, curvature.
Mots-clés : foliation 
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     author = {D. V. Bolotov},
     title = {Topology of codimension-one foliations of nonnegative {curvature.~II}},
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     url = {http://geodesic.mathdoc.fr/item/SM_2014_205_10_a0/}
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D. V. Bolotov. Topology of codimension-one foliations of nonnegative curvature.~II. Sbornik. Mathematics, Tome 205 (2014) no. 10, pp. 1373-1386. http://geodesic.mathdoc.fr/item/SM_2014_205_10_a0/