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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.26 n.1 Antofagasta mayo 2007

http://dx.doi.org/10.4067/S0716-09172007000100001 

Proyecciones Journal of Mathematics
Vol. 26, No 1, pp. 1-25, May 2007.
Universidad Católica del Norte
Antofagasta - Chile



ON SOME INFINITESIMAL AUTOMORPHISMS OF RIEMANNIAN FOLIATION


MOHAMET AlÍ CHAOUCH, TUNISIE
NABILA TORKI - HAMZA UNIVERSITE, TUNISIE


Correspondencia a:


Abstract

In Riemannian foliation, a transverse affine vector field preserves the curvature and its covariant derivatives. In this paper we solve the converse problem. Actually, we show that an infinitesimal automorphism of a Riemannian foliation which preserves the curvature and its covariant derivatives induces a transverse almost homothetic vector field. If in addition the manifold is closed and the foliation is irreducible harmonic , then a such infinitesimal automorphism induces a transverse killing vector field.


Keywords : Riemannian foliation. Harmonic foliation. Irreducible foliation. Transverse vector field. 2
Mohamed Ali Chaouch and Nabila Torki - Hamza

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Mohamed Ali Chaouch
Faculté des Sciences de Bizerte
Université du 7 Novembre A Carthage 7021-Zarzouna.
Bizerte -Tunisie.
e-mail : MohamedAli.Chaouch@fsb.rnu.tn

Nabila Torki-Hamza
Faculté des Sciences de Bizerte
Université du 7 Novembre A Carthage 7021-Zarzouna.
Bizerte -Tunisie.
e-mail : Nabila.Torki-Hamza@fsb.rnu.tn

Received : December 2006. Accepted : February 2007