Topology of codimension-one foliations of nonnegative curvature

Journal Article · Fri May 31 00:00:00 EDT 2013 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2013V204N05ABEH004314· OSTI ID:22122874

Bolotov, Dmitry V ^[1]

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1. B.Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar'kov (Ukraine)

We show that a transversely oriented C{sup 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{sup 2}-foliation with nonnegative sectional curvature. Bibliography: 29 titles.

• OSTI ID: 22122874
• Journal Information: Sbornik. Mathematics, Vol. 204, Issue 5; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
RICCI TENSOR
RIEMANN SPACE
SPHERES
TOPOLOGICAL FOLIATION
TOPOLOGY