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arXiv:0812.3166 [math.DG]AbstractReferencesReviewsResources

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

Marian Ioan Munteanu, Ana Irina Nistor

Published 2008-12-16Version 1

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.

Comments: 15 pages, 6 figures
Journal: Houston J. Mathematics, 37 (2011) 4, 1087-1102
Categories: math.DG
Subjects: 53A05, 53A10, 49Q05
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