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 Balmus–Montaldo–Oniciuc in 2008 for four dimensional hypersurfaces.

中文翻译：

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非零空间形式的四维双调和超曲面具有恒定的平均曲率

摘要 本文通过对Gauss 方程和Codazzi 方程的仔细分析，证明了非零空间形式的四维双调和超曲面具有常数平均曲率。我们的结果对 Balmus-Montaldo-Oniciuc 在 2008 年提出的四维超曲面猜想给出了肯定的答案。