Abstract and Applied Analysis

A Class of Weingarten Surfaces in Euclidean 3-Space

Yu Fu and Lan Li

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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 .

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 398158, 6 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512061

Digital Object Identifier
doi:10.1155/2013/398158

Mathematical Reviews number (MathSciNet)
MR3108639

Zentralblatt MATH identifier
1293.53007

Citation

Fu, Yu; Li, Lan. A Class of Weingarten Surfaces in Euclidean 3-Space. Abstr. Appl. Anal. 2013 (2013), Article ID 398158, 6 pages. doi:10.1155/2013/398158. https://projecteuclid.org/euclid.aaa/1393512061


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