## Abstract and Applied Analysis

### A Class of Weingarten Surfaces in Euclidean 3-Space

Yu Fu and Lan Li

#### Abstract

The class of biconservative surfaces in Euclidean 3-space ${\mathrm{𝔼}}^{\mathrm{3}}$ are defined in (Caddeo et al., 2012) by the equation $A\left(\text{grad\hspace\left\{0.17em\right\}}H\right)=-H\text{\hspace\left\{0.17em\right\}grad\hspace\left\{0.17em\right\}}H$ for the mean curvature function $H$ and the Weingarten operator $A$. In this paper, we consider the more general case that surfaces in ${\mathrm{𝔼}}^{\mathrm{3}}$ satisfying $A\left(\text{grad\hspace\left\{0.17em\right\}}H\right)=kH\text{\hspace\left\{0.17em\right\}grad\hspace\left\{0.17em\right\}}H$ 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 ${\mathrm{𝔼}}^{\mathrm{3}}$.

#### Article information

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

Dates
First available in Project Euclid: 27 February 2014

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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