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

Abstract

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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Published
20.07.2021
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.
Section
Research articles