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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |