Ricci soliton biharmonic hypersurfaces in the Euclidean space
DOI:
https://doi.org/10.37863/umzh.v73i7.495Keywords:
Biharmonic Hypersurfaces, Ricci SolitonAbstract
UDC 515.12
We investigate biharmonic Ricci soliton hypersurfaces (Mn,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 Mn where ξ is a general vector field.
Then we prove that there are no proper biharmonic Ricci soliton hypersurfaces in the Euclidean space En+1 provided that the potential field ξ is either a principal vector in grad H⊥ or ξ=gradH|gradH|.
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