The Ricci Mean Value Of Conformal Vector Fields And Its Application

In this paper,we mainly study the conformal vector fields and its appplication on Riemannian manifold,first we consider the Ricci mean value of the smooth vector fields on a compact oriented Riemannian manifold,the necessary condition for judging a vector field on a Riemannian manifold as a conformal vector field is given,that if a vector field ξis a conformal vector field,then the Ricci mean of ξ is greater than or equal to zero,and we give the classification of Riemannian manifolds when it equals zero.As an application of the above results,We have completely determin the compact locally conformal flat manifold whose Ricci mean value δ(ξ)disappears.