Ricci soliton biharmonic hypersurfaces in the Euclidean space

  • N. Mosadegh Azarbaijan Shahid Madani Univ., Tabriz, Iran
  • E. Abedi Azarbaijan Shahid Madani Univ., Tabriz, Iran
  • M. Ilmakchi Azarbaijan Shahid Madani Univ., Tabriz, Iran
Keywords: Biharmonic Hypersurfaces, Ricci Soliton


UDC 515.12

We investigate biharmonic Ricci soliton hypersurfaces $(M^n, g,\xi, \lambda)$ whose potential field $\xi$ satisfies certain conditions.
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.
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 $\xi=\dfrac{{ \rm{ grad } \,} H}{|{ \rm{ grad } \,} H|}$.


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How to Cite
Mosadegh, N., E. Abedi, and M. Ilmakchi. “Ricci Soliton Biharmonic Hypersurfaces in the Euclidean Space”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 7, July 2021, pp. 931 -37, doi:10.37863/umzh.v73i7.495.
Research articles