Some Moebius Rigidity Theorems For Hypersurfaces In Sⁿ⁺¹

In this thesis we study the global properties of Moebius geometry of hypersurfaces in the sphere space, we get an integral inequality about compact Willmore hypersurfaces in conformal geometry, we also prove three Moebius rigidity theorems by using this integral inequality and give the characterization of the conformal class of Willmore tori by using Moebius invariants. Moreover, we use Moebius geometric method to give a new proof of E.Cartan’s classical theorem about conformally flat hypersurfaces.