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.
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
@article{10_4153_CJM_2016_054_4,
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/}
}
TY - JOUR AU - Folha, Abigail AU - Peñafiel, Carlos TI - Weingarten Type Surfaces in H2 × R and S2 × R JO - Canadian journal of mathematics PY - 2017 SP - 1292 EP - 1311 VL - 69 IS - 6 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2016-054-4/ DO - 10.4153/CJM-2016-054-4 ID - 10_4153_CJM_2016_054_4 ER -
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