june 2019 On surfaces of finite Chen $III$-type
Hassan Al-Zoubi, Mutaz Al-Sabbagh, Stylianos Stamatakis
Bull. Belg. Math. Soc. Simon Stevin 26(2): 177-187 (june 2019). DOI: 10.36045/bbms/1561687560

Abstract

In this paper, we study quadric 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, corresponding to the third fundamental form. We show that helicoids and spheres are the only quadric surfaces of finite $III$-type.

Citation

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Hassan Al-Zoubi. Mutaz Al-Sabbagh. Stylianos Stamatakis. "On surfaces of finite Chen $III$-type." Bull. Belg. Math. Soc. Simon Stevin 26 (2) 177 - 187, june 2019. https://doi.org/10.36045/bbms/1561687560

Information

Published: june 2019
First available in Project Euclid: 28 June 2019

zbMATH: 1049.53007
MathSciNet: MR3975823
Digital Object Identifier: 10.36045/bbms/1561687560

Subjects:
Primary: 53A05 , 53A45

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

Rights: Copyright © 2019 The Belgian Mathematical Society

Vol.26 • No. 2 • june 2019
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