Conformal Rigidity Of Gradient Ricci Solitons And A Property Of A Conformal Flat Hypersurfaces

In this thesis,we study the conformal transformations which preserve the gradient Ricci solitons structure and the value of the principle curvatures and multiplicit of conformal flat hypersurface in onformal flat space,we get the following conclusions:1?We prove a conformal rigidity theorems on gradient Ricci solitons.Moreover,we give a necessary condition for conformal transformation of preserving the Ricci Soliton Structure for higher dimension.2?the values of principal curvature in conformal flat space are exact and the multiplicity is 1 or n-1.