@article{Mosadegh_Abedi_Ilmakchi_2021, title={Ricci soliton biharmonic hypersurfaces in the Euclidean space}, volume={73}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/495}, DOI={10.37863/umzh.v73i7.495}, abstractNote={<p>UDC 515.12</p> <p>We investigate biharmonic Ricci soliton hypersurfaces $(M^n, g,\xi, \lambda)$ whose potential field $\xi$ satisfies certain conditions. <br>We obtain a result based on the average scalar curvature of the compact Ricci soliton hypersurface $M^n$ where $\xi$ is a general vector field. <br>Then we prove that there are no proper biharmonic Ricci soliton hypersurfaces in the Euclidean space $E^{n+1}$ provided that the potential field $\xi$ is either a principal vector in grad $H^\perp$ or $\xi=\dfrac{ \rm{ grad } \,} H}{|{ \rm{ grad } \,} H|}$.</p&gt;}, number={7}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Mosadegh, N. and Abedi, E. and Ilmakchi, M.}, year={2021}, month={Jul.}, pages={931 - 937} }