Abstract
Let x : M n → S n +1 be a compact Willmore hypersurface with two distinct principal curvatures. In this paper, we present a classification of the compact Willmore hypersurfaces, which multiplicities of principal curvatures are greater than one. And if the one of principal curvatures is simple, we give an integral inequality involving the Möbius scalar curvature of x. Particularly, if the Möbius scalar curvature S g is constant, then Sg=n-1k(n-k)-3n-2n2, and x(M n) is Möbius equivalent to Sk(n-kn)×Sn-k(kn), 1 ≤ k < n.
Original language | English |
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Pages (from-to) | 35-45 |
Number of pages | 11 |
Journal | Differential Geometry and its Application |
Volume | 32 |
Issue number | 1 |
DOIs | |
Publication status | Published - Feb 2014 |
Keywords
- 53C40
- Möbius metric
- Möbius scalar curvature
- Willmore hypersurfaces