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Mat. Sb., 2014, Volume 205, Number 10, Pages 3–18 (Mi msb8329)  

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 $n\geq 5$ 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.

DOI: https://doi.org/10.4213/sm8329

Full text: PDF file (567 kB)
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English version:
Sbornik: Mathematics, 2014, 205:10, 1373–1386

Bibliographic databases:

UDC: 515.168
MSC: 53C12, 57R30
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

Citation in format AMSBIB
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