## Abstract

Let x:M^{n}→S^{n+1} be an immersed hypersurface without umbilical point, then one can define the Möbius metric g, the Möbius second fundamental form B and the Blaschke tensor A on the hypersurface M^{n} which are invariant under the Möbius transformation group of S^{n+1}. A hypersurface is called a Willmore hypersurface if it is the critical point of the volume functional of M^{n} with respect to the Möbius metric g. In this paper, we prove that if the hypersurface x is a compact Willmore hypersurface without umbilical point, then [Formula presented] the equality holds if and only if the hypersurface M^{n} is Möbius equivalent to one of the Willmore tori [Formula presented] where the tensor [Formula presented].

Original language | English |
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Article number | 123707 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 484 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Apr 2020 |

## Keywords

- Möbius invariant
- Möbius transformation group
- Willmore hypersurfaces
- Willmore torus

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