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Four dimensional biharmonic hypersurfaces in nonzero space forms have constant mean curvature

Abstract : 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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Submitted on : Wednesday, July 13, 2022 - 2:51:10 PM
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Zhida Guan, Haizhong Li, Luc Vrancken. Four dimensional biharmonic hypersurfaces in nonzero space forms have constant mean curvature. Journal of Geometry and Physics, Elsevier, 2021, 160, pp.103984. ⟨10.1016/j.geomphys.2020.103984⟩. ⟨hal-03722617⟩

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