Several Studies On The Triviality Of Compact Ricci Solitons

In this paper,we consider compact Ricci solitons.The main results are as follows:firstly,by defining a amount ? on a compact Riemannian manifold,we get two necessary conditions for the Riemannian manifold to become a Ricci soliton;then,we give a new proof to the trivialities of compact,shrinking Ricci solitons with vanished Weyl conformal curvature tensor field.