A Class of Weingarten Surfaces in Euclidean 3-Space. (29th September 2013) - Fu, Yu; Li, Lan
Abstract : 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 .