S n + 1 ]]>

摘要

Letx:Mn→Sn+1be an immersed hypersurface without umbilical point, one can define the M?bius metricgonxwhich is invariant under the M?bius transformation group ofSn+1. The scalar curvatureRwith respect togis called the M?bius scalar curvature. In this paper, we study conformally flat hypersurfaces with constant M?bius scalar curvature inSn+1. First, we classify locally the conformally flat hypersurfaces of dimensionn(≥4)with constant M?bius scalar curvature under the M?bius transformation group ofSn+1. Second, we prove that if an umbilic-free conformally flat hypersurface of dimensionn(≥4)with constant M?bius scalar curvatureRis compact, thenR=(n?1)(n?2)r2,0