Given a foliation on a manifold with suitable curvature form, the Euler class of its tangent bundle is explicitly computed whenever it admits an umbilic leaf. If the leaf is compact, then topological obstructions arise by considering foliated manifolds with certain trivial cohomology group. The results fully generalize to distributions tangent to at least one compact umbilic submanifold.
Étant donné une variété feuilletée munie de formes de courbure convenables, nous calculons explicitement sa classe d'Euler dans le cas totalement ombilical. Si la feuille est compacte, nous obtenons des obstructions topologiques dans le cas où certains groupes d'homologie de la variété feuilletée sont triviaux. Les résultats se généralisent aux distributions tangentes à une sous-variété ombilicale.
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Icaro Gonçalves 1; Fabiano Brito 2
@article{CRMATH_2016__354_6_614_0,
author = {Icaro Gon\c{c}alves and Fabiano Brito},
title = {The {Euler} class of an umbilic foliation},
journal = {Comptes Rendus. Math\'ematique},
pages = {614--618},
publisher = {Elsevier},
volume = {354},
number = {6},
year = {2016},
doi = {10.1016/j.crma.2016.03.014},
language = {en},
}
Icaro Gonçalves; Fabiano Brito. The Euler class of an umbilic foliation. Comptes Rendus. Mathématique, Volume 354 (2016) no. 6, pp. 614-618. doi : 10.1016/j.crma.2016.03.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.03.014/
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