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arXiv · 1410.2510

Translation surfaces of linear Weingarten type

Antonio Bueno·Rafael López
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Abstract

We give a relatively simple proof that a translation surface in Euclidean space that satisfies a relation of type $aH+bK=c$, for some real numbers $a,b,c$, where $H$ and $K$ are the mean curvature and the Gauss curvature of the surface, respectively, must have $a=0$ or $b=0$, and thus, $K$ is constant or $H$ is constant. Our method of proof extends to the Lorentzian ambient space.

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Antonio Bueno, Rafael López. 2014-10-09. Translation surfaces of linear Weingarten type. https://arxiv.org/abs/1410.2510

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