Abstract
In the half-space model of hyperbolic space, that is, \({\mathbb{R}^3_{+}=\{(x,y,z)\in\mathbb{R}^3;z > 0\}}\) with the hyperbolic metric, a translation surface is a surface that writes as z = f(x) + g(y) or y = f(x) + g(z), where f and g are smooth functions. We prove that the only minimal translation surfaces (zero mean curvature in all points) are totally geodesic planes.
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R. López was partially supported by MEC-FEDER grant no. MTM2007-61775 and Junta de Andalucía grant no. P09-FQM-5088.
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López, R. Minimal translation surfaces in hyperbolic space. Beitr Algebra Geom 52, 105–112 (2011). https://doi.org/10.1007/s13366-011-0008-z
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DOI: https://doi.org/10.1007/s13366-011-0008-z