Les varietes biriemanniennes
DOI:
https://doi.org/10.22199/S0716-09172000000100007Keywords:
Orthogonal foliation, manifolds, transverse leaves, riemannian product, foliación ortogonal, hojas transversas, producto riemanniano, variedades.Abstract
Let be a complete manifold with a ”parallel” foliation . We show that if this foliation and its orthogonal foliation admit eache one an ”unisection”, then the manifold is riemannian product of transverses leaves.References
[1] M. Berger, P. Gauduchon, E. Mazet : Le spectre d’une variété riemannienne. Lecture Notes in Mathematics N? 194 Berlin Springer Verlag.
[2] Jean Dieudonné : Eléments d’analyse tome 4. Paris Gauthier Villars.
[3] C. Godbillon : Feuilletages - Etudes géométriques 57R université Louis PASTEUR- I. R.. M. A .(C. N. R. S. )- Mai (1985).
[4] R. A. Blumenthal, J. Hebda, de Rham decomposition theorem for foliated manifolds, Ann. Ins. Fourier, 33(2), pp. 183-198, (1983).
[5] R. Hermann, A sufficient condition that a mapping of Riemannian manifolds be a fibre bundle, Proc. A. M. S. 11, pp. 236-242 (1960).
[6] A. Codja, Sur les sections généralisées d’action localement libre de groupes de Lie compacts, Afrika mathematics, série 3 Vol. 11 (a paraître).
[7] A. Besse, Einstein Manifolds, p. 244.
[8] J. Minlor, Morse Theory, Princeton University Press, (1963).
[2] Jean Dieudonné : Eléments d’analyse tome 4. Paris Gauthier Villars.
[3] C. Godbillon : Feuilletages - Etudes géométriques 57R université Louis PASTEUR- I. R.. M. A .(C. N. R. S. )- Mai (1985).
[4] R. A. Blumenthal, J. Hebda, de Rham decomposition theorem for foliated manifolds, Ann. Ins. Fourier, 33(2), pp. 183-198, (1983).
[5] R. Hermann, A sufficient condition that a mapping of Riemannian manifolds be a fibre bundle, Proc. A. M. S. 11, pp. 236-242 (1960).
[6] A. Codja, Sur les sections généralisées d’action localement libre de groupes de Lie compacts, Afrika mathematics, série 3 Vol. 11 (a paraître).
[7] A. Besse, Einstein Manifolds, p. 244.
[8] J. Minlor, Morse Theory, Princeton University Press, (1963).
Published
2017-06-14
How to Cite
[1]
H. Diallo, “Les varietes biriemanniennes”, Proyecciones (Antofagasta, On line), vol. 19, no. 1, pp. 95-104, Jun. 2017.
Issue
Section
Artículos
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.