Ricci soliton biharmonic hypersurfaces in the Euclidean space - Mosadegh, N.; Abedi, E.; Ilmakchi, M. (Ukrains’kyi Matematychnyi Zhurnal, 2021)
UDC 515.12We 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 $H^\perp$ or $ξ=\dfrac{{ \rm{ grad } \,} H}{|{ \rm{ grad } \,} H|}$.