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On surfaces of finite Chen $III$-type
Journal article

On surfaces of finite Chen $III$-type

Hassan Al-Zoubi, Mutaz Al-Sabbagh and Stylianos Stamatakis
01/06/2019

Abstract

Algebraic Geometry Beltrami operator Differential Geometry Mathematics Quadric surfaces space Surfaces in the Euclidean 3 Surfaces of finite Chen type
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.

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