Commun. Korean Math. Soc. 2018; 33(2): 581-590
Online first article January 9, 2018 Printed April 30, 2018
https://doi.org/10.4134/CKMS.c170223
Copyright © The Korean Mathematical Society.
Hassan Al-Zoubi, Khalid M. Jaber, Stylianos Stamatakis
Al-Zaytoonah University of Jordan, Al-Zaytoonah University of Jordan, Aristotle University of Thessaloniki
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
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