Foliations on closed three-dimensional Riemannian manifolds with small modulus of mean curvature of the leaves
- Authors: Bolotov D.V.1
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Affiliations:
- B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine
- Issue: Vol 86, No 4 (2022)
- Pages: 85-102
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/133874
- DOI: https://doi.org/10.4213/im9124
- ID: 133874
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Abstract
We prove that the modulus of mean curvature of the leaves of a transversely orientedfoliation of codimension one with a generalized Reeb component on an oriented smoothclosed three-dimensional Riemannian manifold cannot be everywhere smaller than a certainpositive constant depending on the volume, the maximum value of the sectional curvature,and the injectivity radius of the manifold. This means that foliations withsmall modulus of mean curvature of the leaves are taut.
Keywords
About the authors
Dmitrii Valerevich Bolotov
B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of UkraineDoctor of physico-mathematical sciences, Senior Researcher
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