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2013 A Class of Weingarten Surfaces in Euclidean 3-Space
Yu Fu, Lan Li
Abstr. Appl. Anal. 2013: 1-6 (2013). DOI: 10.1155/2013/398158


The class of biconservative surfaces in Euclidean 3-space 𝔼 3 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 𝔼 3 satisfying A ( grad  H ) = k H  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 𝔼 3 .


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Yu Fu. Lan Li. "A Class of Weingarten Surfaces in Euclidean 3-Space." Abstr. Appl. Anal. 2013 1 - 6, 2013.


Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 1293.53007
MathSciNet: MR3108639
Digital Object Identifier: 10.1155/2013/398158

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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