Translation surfaces of coordinate finite type

Hassan Al-Zoubi; Stylianos Stamatakis; Waseem Al-Mashaleh; Mohammed Awadallah

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arXiv · 1902.03131

Translation surfaces of coordinate finite type

Hassan Al-Zoubi·Stylianos Stamatakis·Waseem Al-Mashaleh·Mohammed Awadallah

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Abstract

We consider translation surfaces in the 3-dimensional Euclidean space which are of coordinate finite type with respect to the third fundamental form $III$, i.e. their position vector $x$ satisfies the relation $\Delta^{III}x = \Lambda x$, where $\Lambda$ is a square matrix of order 3. We show that Sherk's minimal surface is the only translation surface satisfying $\Delta^{III}x = \Lambda x$.

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Hassan Al-Zoubi, Stylianos Stamatakis, Waseem Al-Mashaleh, Mohammed Awadallah. 2019-02-07. Translation surfaces of coordinate finite type. https://arxiv.org/abs/1902.03131

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