| Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms |
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| 摘 要： | Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms, a topic in Lorentzian conformal geometry which parallels the theory of Willmore surfaces in S4, 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.
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Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms |
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| Authors: | Xiang Ma and Peng Wang |
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| Institution: | (1) School of Mathematical Sciences, Peking University, Beijing, 100871, China |
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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 S4, 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. |
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| Keywords: | spacelike Willmore surfaces polar surfaces adjoint transforms duality theorem Willmore 2-spheres |
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