Open AccessRicci soliton biharmonic hypersurfaces in the Euclidean space
Author(s) -
Najma Mosadegh,
Esmaiel Abedi,
Mohammad Ilmakchi
Publication year - 2021
Publication title -
ukraïnsʹkij matematičnij žurnal
Language(s) - English
Resource type - Journals
ISSN - 1027-3190
DOI - 10.37863/umzh.v73i7.495
Subject(s) - biharmonic equation , hypersurface , scalar curvature , mathematics , ricci curvature , soliton , euclidean space , mathematical physics , mathematical analysis , euclidean geometry , curvature , vector field , pure mathematics , physics , geometry , quantum mechanics , boundary value problem , nonlinear system
UDC 515.12We investigate biharmonic Ricci soliton hypersurfaces whose potential field satisfies certain conditions. We obtain a result based on the average scalar curvature of the compact Ricci soliton hypersurface where is a general vector field. Then we prove that there are no proper biharmonic Ricci soliton hypersurfaces in the Euclidean space provided that the potential field is either a principal vector in grad or .