Topology of codimension-one foliations of nonnegative curvature. II

Journal Article · Fri Oct 31 00:00:00 EDT 2014 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2014V205N10ABEH004422· OSTI ID:22364684

Bolotov, D 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 prove that a 3-connected closed manifold M of dimension n≥5 does not admit a codimension-one C{sup 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{sup 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(π,1)-manifold. Bibliography: 13 titles.

• OSTI ID: 22364684
• Journal Information: Sbornik. Mathematics, Vol. 205, Issue 10; 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
MANY-DIMENSIONAL CALCULATIONS
MATHEMATICAL MANIFOLDS
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
SPHERES
TOPOLOGY