A Class of Weingarten Surfaces in Euclidean 3-Space

Yu Fu, Lan Li
2013 Abstract and Applied Analysis  
The class of biconservative surfaces in Euclidean 3-space𝔼3are defined in (Caddeo et al., 2012) by the equationA(grad H)=-H grad Hfor the mean curvature functionHand the Weingarten operatorA. In this paper, we consider the more general case that surfaces in𝔼3satisfyingA(grad H)=kH grad Hfor some constantkare 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 in𝔼3.
doi:10.1155/2013/398158 fatcat:bwae73qbj5g7lgkrfclazg7z2e