Journal for Geometry and Graphics 22 (2018), No. 1, 015--020
Copyright Heldermann Verlag 2018
Ruled Surfaces of Finite Chen-Type
Hassan Al-Zoubi
Dept. of Mathematics, Al-Zaytoonah University, Amman 11733, Jordan
dr.hassanz@zuj.edu.jo
Shadi Al-Zu'bi
Dept. of Computer Science, Al-Zaytoonah University, Amman 11733, Jordan
smalzubi@zuj.edu.jo
Stylianos Stamatakis
Dept. of Mathematics, Aristotle University, 54124 Thessaloniki, Greece
stamata@math.auth.gr
Hani Almimi
Dept. of Computer Science, Al-Zaytoonah University, Amman 11733, Jordan
hani.mimi@zuj.edu.jo
We study ruled surfaces in the 3-dimensional Euclidean space which are of finite III-type, that is, they are of finite type, in the sense of B.-Y. Chen, with respect to the third fundamental form. We show that helicoids are the only ruled surfaces of finite III-type.
Keywords: Surfaces in Euclidean space, surfaces of finite type, Beltrami operator.
MSC: 53A05; 47A75
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