Structure of a leaf of some codimension one riemannian foliation
Annales de l'Institut Fourier, Volume 38 (1988) no. 1, p. 169-174

Some properties of the range on an open leaf $ℒ$ of some codimension-one foliation are shown. They are different from the known properties of the distance of leaves. They imply that leaf $ℒ$ is of fibred type over a complete Riemannian manifold with boundary, as well that there exists some vector field $v$ on $ℒ$. If $v$ is parallel then $ℒ$ is diffeomorphic to ${ℒ}^{\prime }×\mathbf{R}$ and has non-positive curvature.

Quelques propriétés sont démontrées de la “portée” sur une feuille ouverte $ℒ$ d’un feuilletage arbitraire de co-dimension 1; celles-ci diffèrent des propriétés connues de la distance de feuilles. Elles comprennent que la feuille $ℒ$ est d’un type fibré sur une variété riemannienne complète avec marge, ainsi que l’existence d’un champ vectoriel $v$ sur $ℒ$. Si $v$ est parallèle, $ℒ$ est difféomorphe de ${ℒ}^{\prime }×\mathbf{R}$ et d’une courbure non-positive.

@article{AIF_1988__38_1_169_0,
author = {Bugajska, Krystyna},
title = {Structure of a leaf of some codimension one riemannian foliation},
journal = {Annales de l'Institut Fourier},
publisher = {Imprimerie Louis-Jean},
volume = {38},
number = {1},
year = {1988},
pages = {169-174},
doi = {10.5802/aif.1128},
zbl = {0652.53024},
mrnumber = {89f:53052},
language = {en},
url = {http://www.numdam.org/item/AIF_1988__38_1_169_0}
}

Bugajska, Krystyna. Structure of a leaf of some codimension one riemannian foliation. Annales de l'Institut Fourier, Volume 38 (1988) no. 1, pp. 169-174. doi : 10.5802/aif.1128. http://www.numdam.org/item/AIF_1988__38_1_169_0/

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