We investigate biharmonic Ricci soliton hypersurfaces (Mn, g, 𝜉, ⋋) 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 \( \xi =\frac{\operatorname{grad}\kern0.5em H}{\left|\operatorname{grad}\kern0.5em H\right|}. \)
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 7, pp. 931–937, July, 2021. Ukrainian DOI: 10.37863/umzh.v73i7.495.
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Mosadegh, N., Abedi, E. & Ilmakchi, M. Ricci Soliton Biharmonic Hypersurfaces in the Euclidean Space. Ukr Math J 73, 1084–1091 (2021). https://doi.org/10.1007/s11253-021-01978-z
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DOI: https://doi.org/10.1007/s11253-021-01978-z