Geodesic
Weingarten Type Surfaces in H2 × R and S2 × R
Canadian journal of mathematics, Tome 69 (2017) no. 6, pp. 1292-1311

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In this article, we study complete surfaces $\sum $ , isometrically immersed in the product spaces ${{\mathbb{H}}^{2}}\,\times \,\mathbb{R}$ or ${{\mathbb{S}}^{2\,}}\times \,\mathbb{R}$ having positive extrinsic curvature ${{K}_{e}}$ . Let ${{K}_{i}}$ denote the intrinsic curvature of $\sum $ . Assume that the equation $a{{K}_{i\,}}\,+\,b{{K}_{e\,}}\,=\,c$ holds for some real constants $a\,\ne \,0$ , $b\,>\,0$ , and $c$ . The main result of this article states that when such a surface is a topological sphere, it is rotational.
DOI : 10.4153/CJM-2016-054-4
Mots-clés : 53C42, 53C50, Weingarten surface, extrinsic curvature, intrinsic curvature, height estimate, rotationalWeingarten surface 
Folha, Abigail; Peñafiel, Carlos. Weingarten Type Surfaces in H2 × R and S2 × R. Canadian journal of mathematics, Tome 69 (2017) no. 6, pp. 1292-1311. doi: 10.4153/CJM-2016-054-4
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