Abstract
In this paper, we consider the Möbius geometry of locally conformal flat hypersurfaces. First, we prove that any locally conformal flat hypersurface in the sphere Sn+1(n≥4) is a canal hypersurface, which is the envelope of a one-parameter family of principal curvature hyperspheres. Conversely, canal hypersurfaces in Sn+1(n≥3) without umbilical points are locally conformal flat. Finally, by applying the maximum principle, we show that a compact umbilical points hypersurface with isotropic Blaschke tensor in Sn+1(n≥3) is Möbius equivalent to a compact minimal hypersurface with constant scalar curvature in Sn+1.
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