Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms

作者：Ma Xiang^*; Wang Peng

来源：Science in China Series A-Mathematics, 2008, 51(9): 1561-1576.

DOI：10.1007/s11425-008-0052-9

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

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.

• 出版日期2008-9
• 单位北京大学