Certain Conformal-like Infinitesimal Symmetries and the Curvature of a Compact Riemannian Manifold

Abstract

The notion of orthogonally conformal vector field on a Riemannian manifold is introduced. This class of vector fields properly includes the normalization of nowhere zero conformal ones. It is clarified in several examples. An integral inequality which relates the existence of orthogonally conformal vector fields with properties of the Ricci tensor of a compact Riemannian manifold is proved and some applications are shown.