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A Class of Weingarten Surfaces in Euclidean 3‐Space

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  • Yu Fu
  • Lan Li

Abstract

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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  • Yu Fu & Lan Li, 2013. "A Class of Weingarten Surfaces in Euclidean 3‐Space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:398158
    DOI: 10.1155/2013/398158
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