A submanifold $M^n$ of a Euclidean space ${\mathbb{E}}^N$ is called biharmonic if $\mathrm{\Delta }\overrightarrow{H}=0$, where $\overrightarrow{H}$ is the mean curvature vector of $M^n$. A well known conjecture of B.Y. Chen states that the only biharmonic submanifolds of Euclidean spaces are the minimal ones. Ideal submanifolds were introduced by Chen as those which receive the least possible tension at each point. In this paper we prove that every $\delta (r)$-ideal biharmonic hypersurface in the Euclidean space ${\mathbb{E}}^{n+1}$ ($n\ge 3$) is minimal. In this way we generalize a recent result of B.Y. Chen and M.I. Munteanu. In particular, we show that every $\delta (r)$-ideal biconservative hypersurface in Euclidean space ${\mathbb{E}}^{n+1}$ for $n\ge 3$ must be of constant mean curvature.

子流形 ${\mathrm{中号}}^{ñ}$ 欧式空间 ${\mathbb{Ë}}^{ñ}$ 如果被称为双谐波 $\mathrm{\Delta }\overrightarrow{H}=0$，在哪里 $\overrightarrow{H}$ 是的平均曲率向量 ${\mathrm{中号}}^{ñ}$。BY Chen的一个著名猜想指出，欧几里得空间的唯一双调和子流形是最小的。Chen引入了理想的子流形，作为在每个点上承受最小张力的子流形。在本文中，我们证明$\delta （\mathrm{[R}）$欧空间中的理想双调和超曲面 ${\mathbb{Ë}}^{ñ+\mathrm{1个}}$ （$ñ\ge 3$）是最小的。通过这种方式，我们可以概括BY Chen和MI Munteanu的最新结果。特别是，我们表明$\delta （\mathrm{[R}）$欧空间中的理想双保守超曲面 ${\mathbb{Ë}}^{ñ+\mathrm{1个}}$ 对于 $ñ\ge 3$ 必须具有恒定的平均曲率。