Abstract
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 $g=\frac{n}{n-1}(\|II\|^2-n|{\rm tr}II|^2)I$ 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.
Citation
Zhen Guo. Tongzhu Li. Changping Wang. "Classification of hypersurfaces with constant Möbius Ricci curvature in $\mathbb{R}^{n+1}$." Tohoku Math. J. (2) 67 (3) 383 - 403, 2015. https://doi.org/10.2748/tmj/1446818558
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