In this paper we classify the complete rotational special Weingarten surfaces in S2 × ℝ and ℍ2 × ℝ i. e. rotational surfaces in S2 × ℝ and ℍ2 × ℝ whose mean curvature H and extrinsic curvature Ke satisfy H = f(H2 - Ke), for some function f ε c1([0, +∞]) 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. © 2012 Springer-Verlag.
Classification of rotational special Weingarten surfaces of minimal type in S^2 x R and H^2 x R
Morabito, Filippo;
2013-01-01
Abstract
In this paper we classify the complete rotational special Weingarten surfaces in S2 × ℝ and ℍ2 × ℝ i. e. rotational surfaces in S2 × ℝ and ℍ2 × ℝ whose mean curvature H and extrinsic curvature Ke satisfy H = f(H2 - Ke), for some function f ε c1([0, +∞]) 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. © 2012 Springer-Verlag.File in questo prodotto:
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