We consider closed biharmonic hypersurfaces in a Euclidean sphere and prove a rigidity result under a suitable condition on the scalar curvature. Moreover, we establish an integral formula involving the position vector for biharmonic hypersurfaces in space forms. As an application of this formula, we reobtain a result concerning the closed biharmonic hypersurfaces in Euclidean spheres that lie in a closed hemisphere.

中文翻译：

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关于空间形式的双调和超曲面的评论

我们考虑欧几里得球体中的闭双调和超曲面，并证明了在标量曲率的合适条件下的刚性结果。此外，我们建立了一个涉及空间形式双调和超曲面位置向量的积分公式。作为该公式的应用，我们重新获得了关于位于封闭半球的欧几里得球体中的封闭双调和超曲面的结果。