A Class of Weingarten Surfaces in Euclidean 3-Space. (29th September 2013)

• Record Type: Journal Article
• Authors: Fu, Yu; Li, Lan
• Other Names: Došlý Ondřej Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-09-29
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/398158
• Languages: English
• ISSNs: 1085-3375

Abstract

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 .