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New results on the geometry of translation surfaces. (English) Zbl 1204.53005

Summary: We study the second mean curvature for different hypersurfaces in space forms. We furnish some examples and we recall some connections between minimality and biharmonicity. The main result consists in proving that there are no minimal translation surfaces in the Euclidean three-space.

MSC:

53A05 Surfaces in Euclidean and related spaces
53B25 Local submanifolds
53C40 Global submanifolds
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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