Abstract
The conformal geometry of submanifolds in a constant curvature space was well studied in the past 15 years. The first part of this paper presents the system of complete conformal invariants of submanifolds in a general Riemannian space, and the second part presents several conformal rigidity theorems on compact Willmore hypersurfaces. In particular, the conformal class of Willmore tori is characterized using a conformal invariant.
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