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Topology of codimension-one foliations of nonnegative curvature. II
D. V. Bolotov B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar'kov
Abstract:
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:
foliation, Riemannian manifold, curvature.
Received: 17.01.2014
Citation:
D. V. Bolotov, “Topology of codimension-one foliations of nonnegative curvature. II”, Mat. Sb., 205:10 (2014), 3–18; Sb. Math., 205:10 (2014), 1373–1386
Linking options:
https://www.mathnet.ru/eng/sm8329https://doi.org/10.1070/SM2014v205n10ABEH004422 https://www.mathnet.ru/eng/sm/v205/i10/p3
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Abstract page: | 1417 | Russian version PDF: | 448 | English version PDF: | 12 | References: | 75 | First page: | 48 |
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