We study totally geodesic codimension smooth foliations on Lorentzian manifolds. We are in particular interested in the relations between riemannian flows and geodesic foliations. We prove that, up to a -cover, any Seifert bundle admits such a foliation.
Nous étudions les feuilletages lisses totalement géodésiques de codimension des variétés lorentziennes. Nous nous intéressons notamment aux relations entre les flots riemanniens et les feuilletages géodésiques. Nous prouvons que, quitte à prendre un revêtement d’ordre , tout fibré de Seifert possède un tel feuilletage.
Classification: 57R30, 53C50
Keywords: Totally geodesic foliations, riemannian flows
@article{AIF_2005__55_4_1411_0, author = {Mounoud, Pierre}, title = {Feuilletages totalement g\'eod\'esiques, flots riemanniens et vari\'et\'es de {Seifert}}, journal = {Annales de l'Institut Fourier}, pages = {1411--1438}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {55}, number = {4}, year = {2005}, doi = {10.5802/aif.2128}, mrnumber = {2157171}, zbl = {1080.53024}, language = {fr}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2128/} }
TY - JOUR TI - Feuilletages totalement géodésiques, flots riemanniens et variétés de Seifert JO - Annales de l'Institut Fourier PY - 2005 DA - 2005/// SP - 1411 EP - 1438 VL - 55 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2128/ UR - https://www.ams.org/mathscinet-getitem?mr=2157171 UR - https://zbmath.org/?q=an%3A1080.53024 UR - https://doi.org/10.5802/aif.2128 DO - 10.5802/aif.2128 LA - fr ID - AIF_2005__55_4_1411_0 ER -
%0 Journal Article %T Feuilletages totalement géodésiques, flots riemanniens et variétés de Seifert %J Annales de l'Institut Fourier %D 2005 %P 1411-1438 %V 55 %N 4 %I Association des Annales de l’institut Fourier %U https://doi.org/10.5802/aif.2128 %R 10.5802/aif.2128 %G fr %F AIF_2005__55_4_1411_0
Mounoud, Pierre. Feuilletages totalement géodésiques, flots riemanniens et variétés de Seifert. Annales de l'Institut Fourier, Volume 55 (2005) no. 4, pp. 1411-1438. doi : 10.5802/aif.2128. https://aif.centre-mersenne.org/articles/10.5802/aif.2128/
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