Les varietes biriemanniennes

Authors

  • Hassimiou Diallo Ecole Normale Supérieure.

DOI:

https://doi.org/10.22199/S0716-09172000000100007

Keywords:

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.

Author Biography

Hassimiou Diallo, Ecole Normale Supérieure.

Département de Sciences et Technologie.

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).

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.

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