The maximally symmetric surfaces in the 3-torus

Sheng Bai, Vanessa Robins, Chao Wang, Shicheng Wang*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)

    Abstract

    Suppose an orientation-preserving action of a finite group G on the closed surface Σ g of genus g> 1 extends over the 3-torus T3 for some embedding Σ g⊂ T3. Then | G| ≤ 12 (g- 1) , and this upper bound 12 (g- 1) can be achieved for g= n2+ 1 , 3 n2+ 1 , 2 n3+ 1 , 4 n3+ 1 , 8 n3+ 1 , n∈ Z+. The surfaces in T3 realizing a maximal symmetry can be either unknotted or knotted. Similar problems in the non-orientable category are also discussed. The connection with minimal surfaces in T3 is addressed and the situation when the maximally symmetric surfaces above can be realized by minimal surfaces is identified.

    Original languageEnglish
    Pages (from-to)79-95
    Number of pages17
    JournalGeometriae Dedicata
    Volume189
    Issue number1
    DOIs
    Publication statusPublished - 1 Aug 2017

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