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Sbornik: Mathematics, 2013, Volume 204, Issue 5, Pages 621–640
DOI: https://doi.org/10.1070/SM2013v204n05ABEH004314 (Mi sm8116) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Topology of codimension-one foliations of nonnegative curvature

D. V. Bolotov

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar'kov
English version PDF (404 kB) Citations (1)
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DOI: https://doi.org/10.1070/SM2013v204n05ABEH004314
Abstract: We show that a transversely oriented $C^2$-foliation of codimension one with nonnegative Ricci curvature on a closed orientable manifold is a foliation with almost no holonomy. This allows us to decompose the manifold into blocks on which this foliation has a simple structure. We also show that a manifold homeomorphic to a 5-dimensional sphere does not admit a codimension-one $C^2$-foliation with nonnegative sectional curvature.
Bibliography: 29 titles.
Keywords: foliation, Riemannian manifold, curvature.
Received: 02.03.2012 and 28.11.2012
Russian version:
Matematicheskii Sbornik, 2013, Volume 204, Number 5, Pages 3–24
DOI: https://doi.org/10.4213/sm8116
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”, Mat. Sb., 204:5 (2013), 3–24; Sb. Math., 204:5 (2013), 621–640
Citation in format AMSBIB
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    References:57
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