2015 年 67 巻 3 号 p. 383-403
Let $f: M^n\rightarrow \mathbb{R}^{n+1}$ be an immersed umbilic-free hypersurface in an $(n+1)$-dimensional Euclidean space $\mathbb{R}^{n+1}$ with standard metric $I=df\cdot df$. Let $II$ be the second fundamental form of the hypersurface $f$. One can define the Möbius metric $g=\frac{n}{n-1}(\|II\|^2-n|\mathrm{tr}II|^2)I$ on $f$ which is invariant under the conformal transformations (or the Möbius transformations) of $\mathbb{R}^{n+1}$. The sectional curvature, Ricci curvature with respect to the Möbius metric $g$ is called Möbius sectional curvature, Möbius Ricci curvature, respectively. The purpose of this paper is to classify hypersurfaces with constant Möbius Ricci curvature.
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