Surfaces of Revolution and Canal Surfaces with Generalized Cheng–Yau 1-Type Gauss Maps
In the present work, the notion of generalized Cheng–Yau 1-type Gauss map is proposed, which is similar to the idea of generalized 1-type Gauss maps. Based on this concept, the surfaces of revolution and the canal surfaces in the Euclidean three-space are classified. First of all, we show that the G...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/10/1728 |
| _version_ | 1797551462900826112 |
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| author | Jinhua Qian Xueshan Fu Xueqian Tian Young Ho Kim |
| author_facet | Jinhua Qian Xueshan Fu Xueqian Tian Young Ho Kim |
| author_sort | Jinhua Qian |
| collection | DOAJ |
| description | In the present work, the notion of generalized Cheng–Yau 1-type Gauss map is proposed, which is similar to the idea of generalized 1-type Gauss maps. Based on this concept, the surfaces of revolution and the canal surfaces in the Euclidean three-space are classified. First of all, we show that the Gauss map of any surfaces of revolution with a unit speed profile curve is of generalized Cheng–Yau 1-type. At the same time, an oriented canal surface has a generalized Cheng–Yau 1-type Gauss map if, and only if, it is an open part of a surface of revolution or a torus. |
| first_indexed | 2024-03-10T15:45:26Z |
| format | Article |
| id | doaj.art-12ef6bd67f994593bbad45365acb8085 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:45:26Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-12ef6bd67f994593bbad45365acb80852023-11-20T16:26:23ZengMDPI AGMathematics2227-73902020-10-01810172810.3390/math8101728Surfaces of Revolution and Canal Surfaces with Generalized Cheng–Yau 1-Type Gauss MapsJinhua Qian0Xueshan Fu1Xueqian Tian2Young Ho Kim3Department of Mathematics, Northeastern University, Shenyang 110004, ChinaDepartment of Mathematics, Jeju National University, Jeju 63243, KoreaDepartment of Mathematics, Northeastern University, Shenyang 110004, ChinaDepartment of Mathematics, Kyungpook National University, Daegu 41566, KoreaIn the present work, the notion of generalized Cheng–Yau 1-type Gauss map is proposed, which is similar to the idea of generalized 1-type Gauss maps. Based on this concept, the surfaces of revolution and the canal surfaces in the Euclidean three-space are classified. First of all, we show that the Gauss map of any surfaces of revolution with a unit speed profile curve is of generalized Cheng–Yau 1-type. At the same time, an oriented canal surface has a generalized Cheng–Yau 1-type Gauss map if, and only if, it is an open part of a surface of revolution or a torus.https://www.mdpi.com/2227-7390/8/10/1728surface of revolutioncanal surfaceCheng–Yau operatorGauss map |
| spellingShingle | Jinhua Qian Xueshan Fu Xueqian Tian Young Ho Kim Surfaces of Revolution and Canal Surfaces with Generalized Cheng–Yau 1-Type Gauss Maps Mathematics surface of revolution canal surface Cheng–Yau operator Gauss map |
| title | Surfaces of Revolution and Canal Surfaces with Generalized Cheng–Yau 1-Type Gauss Maps |
| title_full | Surfaces of Revolution and Canal Surfaces with Generalized Cheng–Yau 1-Type Gauss Maps |
| title_fullStr | Surfaces of Revolution and Canal Surfaces with Generalized Cheng–Yau 1-Type Gauss Maps |
| title_full_unstemmed | Surfaces of Revolution and Canal Surfaces with Generalized Cheng–Yau 1-Type Gauss Maps |
| title_short | Surfaces of Revolution and Canal Surfaces with Generalized Cheng–Yau 1-Type Gauss Maps |
| title_sort | surfaces of revolution and canal surfaces with generalized cheng yau 1 type gauss maps |
| topic | surface of revolution canal surface Cheng–Yau operator Gauss map |
| url | https://www.mdpi.com/2227-7390/8/10/1728 |
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