Embedding compact surfaces into the 3-dimensional Euclidean space with maximum symmetry

被引：2

作者：

Wang, Chao ^{[1
]}

Wang, ShiCheng ^{[2
]}

Zhang, YiMu ^{[3
]}

Zimmermann, Bruno ^{[4
]}

机构：

[1] Jonsvannsveien 87 B,H0201, N-7050 Trondheim, Norway

[2] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

[3] Jilin Univ, Sch Math, Changchun 130012, Jilin, Peoples R China

[4] Univ Trieste, Dipartimento Matemat & Geosci, I-34100 Trieste, Italy

来源：

SCIENCE CHINA-MATHEMATICS | 2017年 / 60卷 / 09期

基金：

中国国家自然科学基金;

关键词：

finite group action; extendable action; symmetry of surface; maximum order;

D O I：

10.1007/s11425-017-9078-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space a"e(3) are easier to feel by human's intuition. We give the maximum order of finite group actions on (a"e(3), I ) pound among all possible embedded closed/bordered surfaces with given geometric/algebraic genus greater than 1 in a"e(3). We also identify the topological types of the bordered surfaces realizing the maximum order, and find simple representative embeddings for such surfaces.

引用

页码：1599 / 1614

页数：16

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