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

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′×R et d’une courbure non-positive.

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′×R and has non-positive curvature.

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     title = {Structure of a leaf of some codimension one riemannian foliation},
     journal = {Annales de l'Institut Fourier},
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Bugajska, Krystyna. Structure of a leaf of some codimension one riemannian foliation. Annales de l'Institut Fourier, Tome 38 (1988) no. 1, pp. 169-174. doi : 10.5802/aif.1128. https://www.numdam.org/articles/10.5802/aif.1128/

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