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arXiv · 0709.1837

Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms

Xiang Ma·Peng Wang
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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 holds interesting duality theorem. As an application spacelike Willmore 2-spheres are classified. Finally we construct a family of homogeneous spacelike Willmore tori.

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Xiang Ma, Peng Wang. 2007-09-12. Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms. https://doi.org/10.1007/s11425-008-0052-9

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