Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms

Details Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms

2007-09-12

arxiv.org/abs/0709.1837v1

Science in China (Series A), Vol. 51(2008), No. 9, 1561-1576

Mathematics

Differential Geometry

19 pages

Scientific paper

10.1007/s11425-008-0052-9

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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