Classification of hypersurfaces with constant Möbius Ricci curvature in ℝⁿ⁺¹

Let f : Mⁿ → ℝⁿ⁺¹ be an immersed umbilic-free hypersurface in an (n + 1)-dimensional Euclidean space ℝⁿ⁺¹ with standard metric I = df · df. Let II be the second fundamental form of the hypersurface f . One can define the Möbius metric g = n/n^-1 (∥II∥² - n∥trII∥²)I on f which is invariant under the conformal transformations (or the Möbius transformations) of ℝⁿ⁺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.