The L2-Norm of the Euler Class for Foliations on Closed Irreducible Riemannian 3-Manifolds
An upper bound for the $L^2$-norm of the Euler class $e(\cal F)$ of an arbitrary transversely orientable foliation $\cal F$ of codimension one, defined on a three-dimensional closed irreducible orientable Riemannian 3-manifold $M^3$, is given in terms of constants bounding the volume, the radius of...
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| Datum: | 2025 |
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| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2025
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| Online Zugang: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1097 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Zusammenfassung: | An upper bound for the $L^2$-norm of the Euler class $e(\cal F)$ of an arbitrary transversely orientable foliation $\cal F$ of codimension one, defined on a three-dimensional closed irreducible orientable Riemannian 3-manifold $M^3$, is given in terms of constants bounding the volume, the radius of injectivity, the sectional curvature of $M^3$ and the modulus of mean curvature of the leaves. As a consequence, we get only finitely many cohomological classes of the group $H^2(M^3)$ that can be realized by the Euler class $e(\cal F)$ of a two-dimensional transversely oriented foliation $\cal F$ whose leaves have the modulus of mean curvature which is bounded above by the fixed constant $H_0$.
Mathematical Subject Classification 2020: 53C12, 57R30, 53C20 |
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