Ricci soliton biharmonic hypersurfaces in the Euclidean space
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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Copyright (c) 2021 Esmaiel Abedi, Mohammad Ilmakchi
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