On infinitesimal transformations of Weyl manifolds

A Weyl manifold is a conformal manifold equipped with a torsion free connection preserving the conformal structure. In order to make computations in a conformal gauge invariant way, it is better to work with weighted tensors and Weyl’s covariant derivative which will be called prolonged covariant derivative. In this work, by considering the weights of pseudo-quantities, we examine infinitesimal transformations on Weyl manifolds and we obtain some results by using the definition of prolonged (extended) Lie derivative.