Four dimensional biharmonic hypersurfaces in nonzero space forms have constant mean curvature
Résumé
In this paper, through making careful analysis of Gauss and Codazzi equations, we prove that four dimensional biharmonic hypersurfaces in nonzero space forms have constant mean curvature. Our result gives the positive answer to the conjecture proposed by Balmuş–Montaldo–Oniciuc in 2008 for four dimensional hypersurfaces.
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