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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     author = {Folha, Abigail and Pe\~nafiel, Carlos},
     title = {Weingarten {Type} {Surfaces} in {H2} {\texttimes} {R} and {S2} {\texttimes} {R}},
     journal = {Canadian journal of mathematics},
     pages = {1292--1311},
     year = {2017},
     volume = {69},
     number = {6},
     doi = {10.4153/CJM-2016-054-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2016-054-4/}
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