The maximally symmetric surfaces in the 3-torus
The maximally symmetric surfaces in the 3-torus
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DOI：
10.1007/s10711-017-0218-0
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发表时间：
2017-02
影响因子：
0.5
通讯作者：
Sheng Bai;V. Robins;Chao Wang;Shicheng Wang
中科院分区：
文献类型：
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作者：
Sheng Bai;V. Robins;Chao Wang;Shicheng Wang
假设有限群在亏格闭合面上的方向保持作用在 3 环面上延伸以进行某种嵌入。然后，对于 g = n 2 + 1 , 3 n 2 + 1 , 2 n 3 + 1 , 4 n 3 + 1 , 8 n 3 + 1 , n ∈ Z + 可以实现该上界。实现最大对称性的表面可以是无结的或有结的。还讨论了不可定向类别中的类似问题。讨论了与最小曲面的联系，并识别了上述最大对称曲面可以通过最小曲面实现的情况。
Suppose an orientation-preserving action of a finite groupGon the closed surfaceof genusextends over the 3-torusfor some embedding. Then, and this upper boundcan be achieved for g = n 2 + 1 , 3 n 2 + 1 , 2 n 3 + 1 , 4 n 3 + 1 , 8 n 3 + 1 , n ∈ Z + . The surfaces inrealizing a maximal symmetry can be either unknotted or knotted. Similar problems in the non-orientable category are also discussed. The connection with minimal surfaces inis addressed and the situation when the maximally symmetric surfaces above can be realized by minimal surfaces is identified.