Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324:2012
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On foliations of bounded mean curvature on closed three-dimensional Riemannian manifolds

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Dmitry Bolotov
https://orcid.org/0000-0002-8542-9695

Abstract

The notion of a systole of a foliation sys(ℱ) on an arbitrary foliated closed Riemannian manifold (M,ℱ) is introduced. A lower bound on sys(ℱ) for the foliation ℱ on closed 3-dimensional Riemannian manifold M, the modulus of mean curvature of the leaves of which is bounded above by a fixed constant H0 is given. As a consequence, we estimate the number of Reeb components of such a foliation.

Keywords:
Reeb component, foliation, Riemannian manifold, systole, curvature

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How to Cite
Bolotov, D. (2023). On foliations of bounded mean curvature on closed three-dimensional Riemannian manifolds. Proceedings of the International Geometry Center, 16(2), 173-182. https://doi.org/10.15673/pigc.v16i2.2510
Section
Papers
Author Biography

Dmitry Bolotov, B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine