On some infinitesimal automorphisms of Riemannian foliation

• Ali Chaouch, Mohamed ^[1] ; Torki – Hamza, Nabila ^[1]
  1. [1] Université du 7 Novembre À Carthage, Tunisie.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 26, Nº. 1, 2007, págs. 1-25
• Idioma: inglés
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• Resumen

  • 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.