Ruled and quadric surfaces of finite Chen-type

Hassan Al-Zoubi; Stylianos Stamatakis; Hani Almimi

Ruled and quadric surfaces of finite Chen-type

Differential Geometry 2022-02-07 v2

Authors: Hassan Al-Zoubi , Stylianos Stamatakis , Hani Almimi

Abstract

In this paper, we study ruled surfaces and quadrics 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 and spheres are the only ruled and quadric surfaces of finite $III$ -type, respectively.

Keywords

finite type third fundamental form ruled surfaces quadrics helicoids spheres 3-dimensional Euclidean space

Cite

@article{arxiv.1710.07619,
  title  = {Ruled and quadric surfaces of finite Chen-type},
  author = {Hassan Al-Zoubi and Stylianos Stamatakis and Hani Almimi},
  journal= {arXiv preprint arXiv:1710.07619},
  year   = {2022}
}

Comments

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

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