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Science in China Series A: Mathematics

, Volume 51, Issue 9, pp 1561–1576 | Cite as

Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms

  • Xiang Ma
  • Peng Wang
Article

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.

Keywords

spacelike Willmore surfaces polar surfaces adjoint transforms duality theorem Willmore 2-spheres 

MSC(2000)

Primary 53A30 Secondary 53B30 

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Copyright information

© Science in China Press and Springer-Verlag GmbH 2008

Authors and Affiliations

  1. 1.School of Mathematical SciencesPeking UniversityBeijingChina

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