On the Geometry of the Second Fundamental Form of Translation Surfaces in E3

Details On the Geometry of the Second Fundamental Form of Translation Surfaces in E3 On the Geometry of the Second Fundamental Form of Translation Surfaces in E3

2008-12-16

arxiv.org/abs/0812.3166v1

Houston J. Mathematics, 37 (2011) 4, 1087-1102

Mathematics

Differential Geometry

15 pages, 6 figures

Scientific paper

In this paper we study the second fundamental form of translation surfaces in
E3. We give a non-existence result for polynomial translation surfaces in E3
with vanishing second Gaussian curvature KII. We classify those translation
surfaces for which KII and H are proportional. Finally we obtain that there are
no II-minimal translation surfaces in the Euclidean 3-space.

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