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 d’un feuilletage arbitraire de co-dimension 1; celles-ci diffèrent des propriétés connues de la distance de feuilles. Elles comprennent que la feuille est d’un type fibré sur une variété riemannienne complète avec marge, ainsi que l’existence d’un champ vectoriel v sur . Si v est parallèle, est difféomorphe de ×R et d’une courbure non-positive.

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

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     title = {Structure of a leaf of some codimension one riemannian foliation},
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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. http://archive.numdam.org/articles/10.5802/aif.1128/

[1] R.A. Blumenthal, J.J. Hebda. — Complementary distributions which preserve the leaf geometry and applications to totally geodesic foliation, Quart. J. Math. Oxford, (2) 35 (1984), 383-392. | MR | Zbl

[2] D. Gromoll, W. Meyer. — On complete open manifolds of positive curvature, Ann. Math., 90 (1969), 75-90. | MR | Zbl

[3] D.I. Jonson, L.B. Whitt. — Totally geodesic foliations, J. Diff. Geom., 15 (1980), 225-235. | MR | Zbl

[4] S. Kashiwabara. — The structure of a Riemannian manifold admitting a parallel field of one dimensional tangent vector subspaces, Tohoku Math. J., 11 (1959), 119-132. | MR | Zbl

[5] S. Kobayashi, K. Nomizu. — Foundations of differential geometry, vol. I, Interscience, New York, 1967.

[6] B.L. Reinhart. — Foliated manifolds with bundle like metrics, Annals of Math., 69 (1959), 119-132. | MR | Zbl

[7] D.J. Welsh. — On the existence of complete parallel vector fields, Proc. Am. Math. Soc., 97 (1986), 311-314. | MR | Zbl

[8] S.T. Yau. — Remarks on the group of isometries of a Riemannian manifold, Topology, 16 (1977), 239-247. | MR | Zbl

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