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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

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CHAOUCH, MOHAMET AlÍ  y  TORKI - HAMZA, NABILA. ON SOME INFINITESIMAL AUTOMORPHISMS OF RIEMANNIAN FOLIATION. Proyecciones (Antofagasta) [online]. 2007, vol.26, n.1, pp. 01-25. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172007000100001.

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.

Palabras clave : Riemannian foliation; Harmonic foliation; Irreducible foliation; Transverse vector field.

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