Abstract
Let M(Sn+1) denote the Möbius transformation group of the (n+1)-dimensional sphere Sn+1. A hypersurface x:Mn→Sn+1 is called a Möbius homogeneous hypersurface if there exists a subgroup G of M(Sn+1) such that the orbit G⋅p=x(Mn),p∈x(Mn). In this paper, the Möbius homogeneous hypersurfaces are classified completely up to a Möbius transformation of Sn+1.
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