Helicoids in 𝕊2× ℝ and ℍ2× ℝ
| Autor: | Young Wook Kim, Seong Deog Yang, Heayong Shin, Sung Eun Koh |
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| Rok vydání: | 2009 |
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| Zdroj: | Pacific Journal of Mathematics. 242:281-297 |
| ISSN: | 0030-8730 |
| DOI: | 10.2140/pjm.2009.242.281 |
| Popis: | We provide two characterizations of helicoids in S 2 x ℝ and in ℍ 2 x ℝ. First, we show that any nontrivial ruled minimal surface in S 2 x ℝ and in ℍ 2 × ℝ is a part of a helicoid. Second, we also show that these surfaces can be characterized as the only surface with zero mean curvature with respect to both the Riemannian product metric and the Lorentzian product metric on S 2 x ℝ or ℍ 2 x ℝ. |
| Databáze: | OpenAIRE |
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