Communications of the
Korean Mathematical Society CKMS

In this paper, we consider surfaces in the 3-dimensional Euclidean space $ \mathbb{E}^{3}$ which are of finite $III$-type, that is, they are of finite type, in the sense of B.-Y. Chen, corresponding to the third fundamental form. We present an important family of surfaces, namely, tubes in $\mathbb{E}^{3}$. We show that tubes are of infinite $III$-type.

Keywords: surfaces in the Euclidean 3-space, surfaces of finite Chen-type, Beltrami operator

MSC numbers: 53A05