an:06306796
Zbl 1293.53007
Fu, Yu; Li, Lan
A class of Weingarten surfaces in Euclidean 3-space
EN
Abstr. Appl. Anal. 2013, Article ID 398158, 6 p. (2013).
00317499
2013
j
53A07
mean curvature; Weingarten operator; bi-conservative surfaces; linear Weingarten surfaces
Summary: The class of biconservative surfaces in Euclidean 3-space \(\mathbb E^3\) was defined by \textit{R. Caddeo} et al. in [Ann. Mat. Pura Appl. (4) 193, No. 2, 529--550 (2014; Zbl 1294.53006)] by the equation \(A(\mathrm{grad}H)=-H\mathrm{grad}H\) for the mean curvature function \(H\) and the Weingarten operator \(A\). In this paper, we consider the more general case that surfaces in \(\mathbb E^3\) satisfying \(A(\mathrm{grad}H)=kH\mathrm{grad}H\) 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 \(\mathbb E^3\).
Zbl 1294.53006