Embedding compact surfaces into the 3-dimensional Euclidean space with maximum symmetry
The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space R3 are easier to feel by human's intuition. We give the maximum order of finite group actions on (R3 E) among all possible embedded closed/bordered surfaces with given geometric/algebraic genus...
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Veröffentlicht in: | Science China. Mathematics 2017-09, Vol.60 (9), p.1599-1614 |
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creator | Wang, Chao Wang, ShiCheng Zhang, YiMu Zimmermann, Bruno |
description | The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space R3 are easier to feel by human's intuition. We give the maximum order of finite group actions on (R3 E) among all possible embedded closed/bordered surfaces with given geometric/algebraic genus greater than 1 in R3. We also identify the topological types of the bordered surfaces realizing the maximum order, and findsimple representative embeddings for such surfaces. |
doi_str_mv | 10.1007/s11425-017-9078-0 |
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We also identify the topological types of the bordered surfaces realizing the maximum order, and findsimple representative embeddings for such surfaces.</description><subject>Applications of Mathematics</subject><subject>Euclidean geometry</subject><subject>Euclidean space</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>三维欧氏空间</subject><subject>三维立体空间</subject><subject>对称性</subject><subject>嵌入</subject><subject>拓扑类型</subject><subject>曲面</subject><subject>群作用</subject><subject>表面</subject><issn>1674-7283</issn><issn>1869-1862</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp9UMtOwzAQtBBIVNAP4GbB2bB-JE6OqCoPqRIXEEcrsZ3WVZ20diLo3-MoFeLEHvYhzezODkI3FO4pgHyIlAqWEaCSlCALAmdoRou8JCmx89TnUhDJCn6J5jFuIQUvQUg-Q59LX1tjXLvGuvP7Svc4DqGptI3YtX2H-43FnBjnbRtd11Y7vBz0zhlbtTgmvMVfrt9gX307P3gcj97bPhyv0UVT7aKdn-oV-nhavi9eyOrt-XXxuCKaC96TOjdZwes8E7kwFgooSi0oazhnFFhTcAo16Kwxo1zQTS7SaCqRG1NYJjN-he6mvfvQHQYbe7XthpBkRkVLnh7nUowoOqF06GIMtlH74HwVjoqCGi1Uk4UqWahGCxUkDps4MWHbtQ1_Nv9Duj0d2nTt-pB4v5eSFKBlmVP-A9a-fow</recordid><startdate>20170901</startdate><enddate>20170901</enddate><creator>Wang, Chao</creator><creator>Wang, ShiCheng</creator><creator>Zhang, YiMu</creator><creator>Zimmermann, Bruno</creator><general>Science China Press</general><general>Springer Nature B.V</general><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>~WA</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20170901</creationdate><title>Embedding compact surfaces into the 3-dimensional Euclidean space with maximum symmetry</title><author>Wang, Chao ; Wang, ShiCheng ; Zhang, YiMu ; Zimmermann, Bruno</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c343t-b6d583b65464de08089c412f332102f8310b0c5fd90470cf64b0cda46dd8e2753</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Applications of Mathematics</topic><topic>Euclidean geometry</topic><topic>Euclidean space</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>三维欧氏空间</topic><topic>三维立体空间</topic><topic>对称性</topic><topic>嵌入</topic><topic>拓扑类型</topic><topic>曲面</topic><topic>群作用</topic><topic>表面</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Chao</creatorcontrib><creatorcontrib>Wang, ShiCheng</creatorcontrib><creatorcontrib>Zhang, YiMu</creatorcontrib><creatorcontrib>Zimmermann, Bruno</creatorcontrib><collection>中文科技期刊数据库</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>中文科技期刊数据库-7.0平台</collection><collection>中文科技期刊数据库- 镜像站点</collection><collection>CrossRef</collection><jtitle>Science China. 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subjects | Applications of Mathematics Euclidean geometry Euclidean space Mathematics Mathematics and Statistics 三维欧氏空间 三维立体空间 对称性 嵌入 拓扑类型 曲面 群作用 表面 |
title | Embedding compact surfaces into the 3-dimensional Euclidean space with maximum symmetry |
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