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Mat. Zametki, 1998, Volume 63, Issue 5, Pages 651–659 (Mi mz1330)  

This article is cited in 2 scientific papers (total in 2 papers)

Hyperfoliations on compact 3-manifolds with restrictions on the external curvature of leaves

D. V. Bolotov

Kharkiv State University

Abstract: $C^\infty$-foliations of codimension 1 on compact Riemannian 3-manifolds are studied. New classes of foliations, namely hyperbolic, elliptic, and parabolic foliations, are considered. Examples of such foliations are presented. In particular, a $C^\infty$-metric of nonnegative sectional curvature on $S^3$ such that the Reeb foliation is parabolic with respect to this metric is constructed. Analytic 3-manifolds with sectional curvature of constant sign admitting parabolic foliations are classified.

DOI: https://doi.org/10.4213/mzm1330

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English version:
Mathematical Notes, 1998, 63:5, 575–581

Bibliographic databases:

UDC: 514
Received: 03.09.1996

Citation: D. V. Bolotov, “Hyperfoliations on compact 3-manifolds with restrictions on the external curvature of leaves”, Mat. Zametki, 63:5 (1998), 651–659; Math. Notes, 63:5 (1998), 575–581

Citation in format AMSBIB
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\by D.~V.~Bolotov
\paper Hyperfoliations on compact 3-manifolds with restrictions on the external curvature of leaves
\jour Mat. Zametki
\yr 1998
\vol 63
\issue 5
\pages 651--659
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\crossref{https://doi.org/10.4213/mzm1330}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1683637}
\zmath{https://zbmath.org/?q=an:0956.53025}
\transl
\jour Math. Notes
\yr 1998
\vol 63
\issue 5
\pages 575--581
\crossref{https://doi.org/10.1007/BF02312836}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Borisenko, “Extrinsic geometry of parabolic and saddle multidimensional manifolds”, Russian Math. Surveys, 53:6 (1998), 1111–1158  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. V. Krouglov, “Parabolic foliations on three-manifolds”, Zhurn. matem. fiz., anal., geom., 5:2 (2009), 170–191  mathnet  mathscinet  zmath
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