In this paper we classify Euclidean hypersurfaces $f\colon M^n \rightarrow \mathbb{R}^{n+1}$ with a principal curvature of multiplicity $n-2$ that admit a genuine conformal deformation $\tilde{f}\colon M^n \rightarrow \mathbb{R}^{n+2}$. That $\tilde{f}\colon M^n \rightarrow \mathbb{R}^{n+2}$ is a genuine conformal deformation of $f$ means that it is a conformal immersion for which there exists no open subset $U \subset M^n$ such that the restriction $\tilde{f}|_U$ is a composition $\tilde f|_U=h\circ f|_U$ of $f|_U$ with a conformal immersion $h\colon V\to \mathbb{R}^{n+2}$ of an open subset $V\subset \mathbb{R}^{n+1}$ containing $f(U)$.

中文翻译：

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在第二维中具有真正共形变形的欧几里得超曲面

在本文中，我们对欧几里得超曲面 $f\colon M^n \rightarrow \mathbb{R}^{n+1}$ 进行分类，主曲率的多重性 $n-2$ 允许真正的共形变形 $\tilde{f }\colon M^n \rightarrow \mathbb{R}^{n+2}$。$\tilde{f}\colon M^n \rightarrow \mathbb{R}^{n+2}$ 是 $f$ 的真正共形变形意味着它是一个共形浸没，不存在开放子集 $ U \subset M^n$ 使得限制 $\tilde{f}|_U$ 是 $f|_U$ 的组合 $\tilde f|_U=h\circ f|_U$ 与保形浸入 $h\包含 $f(U)$ 的开放子集 $V\subset \mathbb{R}^{n+1}$ 的冒号 V\to \mathbb{R}^{n+2}$。