Compact Willmore hypersurfaces with two distinct principal curvatures in S n +1

Tongzhu Li*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Let x : M nS 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 languageEnglish
Pages (from-to)35-45
Number of pages11
JournalDifferential Geometry and its Application
Volume32
Issue number1
DOIs
Publication statusPublished - Feb 2014

Keywords

  • 53C40
  • Möbius metric
  • Möbius scalar curvature
  • Willmore hypersurfaces

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