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arXiv · 1710.07619

Ruled and quadric surfaces of finite Chen-type

Hassan Al-Zoubi·Stylianos Stamatakis·Hani Almimi
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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.

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Hassan Al-Zoubi, Stylianos Stamatakis, Hani Almimi. 2017-10-19. Ruled and quadric surfaces of finite Chen-type. https://arxiv.org/abs/1710.07619

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