Ricci soliton biharmonic hypersurfaces in the Euclidean space
UDC 515.12 We investigate biharmonic Ricci soliton hypersurfaces (M^n, g,ξ, λ) whose potential field ξ satisfies certain conditions. We obtain a result based on the average scalar curvature of the compact Ricci soliton hypersurface M^n where ξ is a general vector field. Then we prove that there are no proper biharmonic Ricci soliton hypersurfaces in the Euclidean space E^n+1 provided that the potential field ξ is either a principal vector in grad H^ or ξ= grad H