A Class of Weingarten Surfaces in Euclidean 3-Space
The class of biconservative surfaces in Euclidean 3-space 𝔼3 are defined in (Caddeo et al., 2012) by the equation A(grad H)=-H grad H for the mean curvature function H and the Weingarten operator A. In this paper, we consider the more general case that surfaces in 𝔼3 satisfying A(grad H)=kH grad H...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/398158 |
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| author | Yu Fu Lan Li |
| author_facet | Yu Fu Lan Li |
| author_sort | Yu Fu |
| collection | DOAJ |
| description | The class of biconservative surfaces in Euclidean 3-space 𝔼3 are defined in (Caddeo et al., 2012) by the equation A(grad H)=-H grad H for the mean curvature function H and the Weingarten operator A. In this paper, we consider the more general case that surfaces in 𝔼3 satisfying A(grad H)=kH grad H for some constant k are called generalized bi-conservative surfaces. We show that this class of surfaces are linear Weingarten surfaces. We also give a complete classification of generalized bi-conservative surfaces in 𝔼3. |
| format | Article |
| id | doaj-art-03b2bfb9dd064c9da568305d812e48a9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-03b2bfb9dd064c9da568305d812e48a92025-02-03T01:22:47ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/398158398158A Class of Weingarten Surfaces in Euclidean 3-SpaceYu Fu0Lan Li1School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Dalian 116025, ChinaCollege of Mathematics and Computational Science, Shenzhen University, Shenzhen 518060, ChinaThe class of biconservative surfaces in Euclidean 3-space 𝔼3 are defined in (Caddeo et al., 2012) by the equation A(grad H)=-H grad H for the mean curvature function H and the Weingarten operator A. In this paper, we consider the more general case that surfaces in 𝔼3 satisfying A(grad H)=kH grad H for some constant k are called generalized bi-conservative surfaces. We show that this class of surfaces are linear Weingarten surfaces. We also give a complete classification of generalized bi-conservative surfaces in 𝔼3.http://dx.doi.org/10.1155/2013/398158 |
| spellingShingle | Yu Fu Lan Li A Class of Weingarten Surfaces in Euclidean 3-Space Abstract and Applied Analysis |
| title | A Class of Weingarten Surfaces in Euclidean 3-Space |
| title_full | A Class of Weingarten Surfaces in Euclidean 3-Space |
| title_fullStr | A Class of Weingarten Surfaces in Euclidean 3-Space |
| title_full_unstemmed | A Class of Weingarten Surfaces in Euclidean 3-Space |
| title_short | A Class of Weingarten Surfaces in Euclidean 3-Space |
| title_sort | class of weingarten surfaces in euclidean 3 space |
| url | http://dx.doi.org/10.1155/2013/398158 |
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