ON SOME INFINITESIMAL AUTOMORPHISMS OF RIEMANNIAN FOLIATION - CHAOUCH,MOHAMET AlÍ (Universidad Católica del Norte, Departamento de Matemáticas, 2007)
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.