Classification of rotational special Weingarten surfaces of minimal type in {\mathbb{S}^2 \times \mathbb{R}} and {\mathbb{H}^2 \times \mathbb{R}} |
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Authors: | Filippo Morabito M Magdalena Rodríguez |
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Institution: | 1. School of Mathematics, Korea Institute for Advanced Study, Hoegiro 87, Cheongnyangni 2-dong, Seoul, 130-722, South Korea 2. Departamento de Geometría y Topología, Universidad de Granada, Campus de Fuentenueva s/n, 18071, Granada, Spain
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Abstract: | In this paper we classify the complete rotational special Weingarten surfaces in ${\mathbb{S}^2 \times \mathbb{R}}$ and ${\mathbb{H}^2 \times \mathbb{R}}$ ; i.e. rotational surfaces in ${\mathbb{S}^2 \times \mathbb{R}}$ and ${\mathbb{H}^2 \times \mathbb{R}}$ whose mean curvature H and extrinsic curvature K e satisfy H = f(H 2 ? K e ), for some function ${f \in \mathcal{C}^1(0,+\infty))}$ such that f(0) = 0 and 4x(f′(x))2 < 1 for any x ≥ 0. Furthermore we show the existence of non-complete examples of such surfaces. |
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