[La class d'Euler d'un feuilletage totalement ombilical]
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.
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.
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@article{CRMATH_2016__354_6_614_0,
author = {Gon\c{c}alves, Icaro and Brito, Fabiano},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2016.03.014/}
}
TY - JOUR AU - Gonçalves, Icaro AU - Brito, Fabiano TI - The Euler class of an umbilic foliation JO - Comptes Rendus. Mathématique PY - 2016 SP - 614 EP - 618 VL - 354 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.03.014/ DO - 10.1016/j.crma.2016.03.014 LA - en ID - CRMATH_2016__354_6_614_0 ER -
%0 Journal Article %A Gonçalves, Icaro %A Brito, Fabiano %T The Euler class of an umbilic foliation %J Comptes Rendus. Mathématique %D 2016 %P 614-618 %V 354 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2016.03.014/ %R 10.1016/j.crma.2016.03.014 %G en %F CRMATH_2016__354_6_614_0
Gonçalves, Icaro; Brito, Fabiano. The Euler class of an umbilic foliation. Comptes Rendus. Mathématique, Tome 354 (2016) no. 6, pp. 614-618. doi : 10.1016/j.crma.2016.03.014. http://www.numdam.org/articles/10.1016/j.crma.2016.03.014/
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