Möbius Homogeneous Hypersurfaces in ${\mathbb{S}}^{n+1}$

Abstract

Let $\mathbb{M}({\mathbb{S}}^{n+1})$ denote the Möbius transformation group of the $(n+1)$-dimensional sphere ${\mathbb{S}}^{n+1}$. A hypersurface $x:M^n\to {\mathbb{S}}^{n+1}$ is called a Möbius homogeneous hypersurface if there exists a subgroup $G$ of $\mathbb{M}({\mathbb{S}}^{n+1})$ such that the orbit $G\cdot p=x(M^n),p\in x(M^n)$. In this paper, the Möbius homogeneous hypersurfaces are classified completely up to a Möbius transformation of ${\mathbb{S}}^{n+1}$.

35 pages, comments welcome