Authors discover that a spacelike surface in Minkowski 3-space is related to a integrable system. They obtain a representation formula for spacelike surfaces with prescribed mean curvature. This representation formula...Authors discover that a spacelike surface in Minkowski 3-space is related to a integrable system. They obtain a representation formula for spacelike surfaces with prescribed mean curvature. This representation formula is equivalent to that obtained ly Akutagawa and Nishikawa.展开更多
Let Ep^2＋p（resp.E2^2＋p） be a （2＋p）-dimensional pseudo-Euclidean space with the index p （resp.2）. The maximal spacelike or minimal timelike translation surfaces M^2 in Ep^2＋p or E2^2＋p are considered and a c...Let Ep^2＋p（resp.E2^2＋p） be a （2＋p）-dimensional pseudo-Euclidean space with the index p （resp.2）. The maximal spacelike or minimal timelike translation surfaces M^2 in Ep^2＋p or E2^2＋p are considered and a complete classification is given.展开更多
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 tr...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.展开更多
文摘Authors discover that a spacelike surface in Minkowski 3-space is related to a integrable system. They obtain a representation formula for spacelike surfaces with prescribed mean curvature. This representation formula is equivalent to that obtained ly Akutagawa and Nishikawa.
文摘Let Ep^2＋p（resp.E2^2＋p） be a （2＋p）-dimensional pseudo-Euclidean space with the index p （resp.2）. The maximal spacelike or minimal timelike translation surfaces M^2 in Ep^2＋p or E2^2＋p are considered and a complete classification is given.
基金supported by the National Natural Science Foundation of China (Grant No. 10771005)
文摘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.
