Chen-Gackstatter type surfaces in R^4_1: deformation, symmetry, and embeddedness
Chen-Gackstatter type surfaces in R^4_1: deformation, symmetry, and embeddedness
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发表时间：
2012-12
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通讯作者：
Zhenxiao Xie;Xiang Ma
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作者：
Zhenxiao Xie;Xiang Ma
我们明确地在经典Chen-Gackstatter曲面的R^4＿1上找到了一个2参数变形族，并证明了一个更大的4参数变形族的存在。它们中的每一个仍然有一个属1，一个唯一的端点，有全高斯曲率$-\int K=8\pi$。另一方面，当我们假设曲面具有4个以上的对称性时，得到了一个唯一性定理。本文还讨论了嵌入性问题，并给出了部分结果。
We find a 2-parameter family of deformations in R^4_1 of the classical Chen-Gackstatter surface explicitly, and show the existence of a larger 4-parameter family of deformations. Each of them still has genus one, a unique end, with total Gaussian curvature $-\int K=8\pi$. On the other hand, a uniqueness theorem is obtained when we assume that the surface has more than 4 symmetries. The problem of embeddedness is also discussed with some partial results.