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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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2025
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oai:jmag.ilt.kharkiv.ua:article-10972025-12-08T18:45:53Z The L2-Norm of the Euler Class for Foliations on Closed Irreducible Riemannian 3-Manifolds The L2 -Norm of the Euler Class for Foliations on Closed Irreducible Riemannian 3-Manifolds The L2-Norm of the Euler Class for Foliations on Closed Irreducible Riemannian 3-Manifolds Bolotov, Dmitry V. 3-вимірний многовид шарування клас Ейлера середня кривина 3-manifold foliation Euler class mean curvature 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 An upper bound for the $L^2$-norm of the Euler class $e(\F)$ of an arbitrary transversely orientable foliation $\F$ 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 cohomolo\-gical classes of the group $H^2(M^3)$ that can be realized by the Euler class $e(\F)$ of a two-dimensional transversely oriented foliation $\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 Через сталі, що обмежують об'єм, радіус ін'єктивності, секційну кривизну многовиду та модуль середньої кривини шарів, наведено верхню межу $L^2$-норми класу Ейлера $e(\cal F)$ довільного трансверсально орієнтованого шарування $\cal F$ ковимірності один, визначеного на тривимірному замкненому незвідному орієнтованому рімановому тривимірному многовиді $M^3$. Як наслідок, маємо тільки скінченну кількість когомологічних класів групи $H^2(M^3)$, які можуть бути реалізовані класом Ейлера $e(\cal F)$ двовимірного трансверсально орієнтованого шарування $\cal F$, шари якого мають модуль середньої кривини, обмежений зверху фіксованою константою $H_0$. Mathematical Subject Classification 2020: 53C12, 57R30, 53C20 Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2025-05-17 Article Article application/pdf https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1097 10.15407/mag21.02.01 Journal of Mathematical Physics, Analysis, Geometry; Vol. 21 No. 2 (2025); 135-159 Журнал математической физики, анализа, геометрии; Том 21 № 2 (2025); 135-159 Журнал математичної фізики, аналізу, геометрії; Том 21 № 2 (2025); 135-159 1817-5805 1812-9471 en https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1097/jm21-0135e Авторське право (c) 2025 Журнал математичної фізики, аналізу, геометрії |
| institution |
Journal of Mathematical Physics, Analysis, Geometry |
| baseUrl_str |
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| datestamp_date |
2025-12-08T18:45:53Z |
| collection |
OJS |
| language |
English |
| topic |
3-вимірний многовид шарування клас Ейлера середня кривина |
| spellingShingle |
3-вимірний многовид шарування клас Ейлера середня кривина Bolotov, Dmitry V. The L2-Norm of the Euler Class for Foliations on Closed Irreducible Riemannian 3-Manifolds |
| topic_facet |
3-вимірний многовид шарування клас Ейлера середня кривина 3-manifold foliation Euler class mean curvature |
| format |
Article |
| author |
Bolotov, Dmitry V. |
| author_facet |
Bolotov, Dmitry V. |
| author_sort |
Bolotov, Dmitry V. |
| title |
The L2-Norm of the Euler Class for Foliations on Closed Irreducible Riemannian 3-Manifolds |
| title_short |
The L2-Norm of the Euler Class for Foliations on Closed Irreducible Riemannian 3-Manifolds |
| title_full |
The L2-Norm of the Euler Class for Foliations on Closed Irreducible Riemannian 3-Manifolds |
| title_fullStr |
The L2-Norm of the Euler Class for Foliations on Closed Irreducible Riemannian 3-Manifolds |
| title_full_unstemmed |
The L2-Norm of the Euler Class for Foliations on Closed Irreducible Riemannian 3-Manifolds |
| title_sort |
l2-norm of the euler class for foliations on closed irreducible riemannian 3-manifolds |
| title_alt |
The L2-Norm of the Euler Class for Foliations on Closed Irreducible Riemannian 3-Manifolds The L2 -Norm of the Euler Class for Foliations on Closed Irreducible Riemannian 3-Manifolds |
| description |
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 |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України |
| publishDate |
2025 |
| url |
https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1097 |
| work_keys_str_mv |
AT bolotovdmitryv thel2normoftheeulerclassforfoliationsonclosedirreducibleriemannian3manifolds AT bolotovdmitryv l2normoftheeulerclassforfoliationsonclosedirreducibleriemannian3manifolds |
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2025-09-27T01:57:14Z |
| last_indexed |
2025-12-17T12:06:06Z |
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1851757078939435008 |