Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms

Xiang Ma, Peng Wang

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13 Scopus citations

Abstract

Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms, a topic in Lorentzian conformal geometry which parallels the theory of Willmore surfaces in S 4, are studied in this paper. We define two kinds of transforms for such a surface, which produce the so-called left/right polar surfaces and the adjoint surfaces. These new surfaces are again conformal Willmore surfaces. For them the interesting duality theorem holds. As an application spacelike Willmore 2-spheres are classified. Finally we construct a family of homogeneous spacelike Willmore tori.

Original languageEnglish
Pages (from-to)1561-1576
Number of pages16
JournalScience in China, Series A: Mathematics
Volume51
Issue number9
DOIs
StatePublished - Sep 2008
Externally publishedYes

Keywords

  • Adjoint transforms
  • Duality theorem
  • Polar surfaces
  • Spacelike Willmore surfaces
  • Willmore 2-spheres

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