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Sbornik: Mathematics, 2014, Volume 205, Issue 10, Pages 1373–1386
DOI: https://doi.org/10.1070/SM2014v205n10ABEH004422
(Mi sm8329)
 

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
References:
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
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 10, Pages 3–18
DOI: https://doi.org/10.4213/sm8329
Bibliographic databases:
Document Type: Article
UDC: 515.168
MSC: 53C12, 57R30
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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  • 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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