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Ruled minimal
surfaces in the three-dimensional Heisenberg group
Heayong Shin, Young Wook Kim, Sung-Eun Koh, Hyung Yong Lee and Seong-Deog Yang |
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Vol. 261 (2013), No. 2, 477–496
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Abstract |
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It is shown that parts of planes, helicoids and hyperbolic paraboloids are the only minimal surfaces ruled by geodesics in the three-dimensional Riemannian Heisenberg group. It is also shown that they are the only surfaces in the three-dimensional Heisenberg group whose mean curvature is zero with respect to both the standard Riemannian metric and the standard Lorentzian metric. |
Keywords
Heisenberg group, ruled surface, minimal surface
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Mathematical Subject Classification 2010
Primary: 53A35
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Milestones
Received: 6 October 2011
Revised: 14 September 2012
Accepted: 24 September 2012
Published: 20 March 2013
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Authors |
| Heayong Shin | |
| Department of Mathematics Chung-Ang University Seoul 156-756 South Korea |
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| Young Wook Kim | |
| Department of Mathematics Korea University Seoul 136-701 South Korea |
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| Sung-Eun Koh | |
| Department of Mathematics Konkuk University Seoul 143-701 South Korea |
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| Hyung Yong Lee | |
| Department of Mathematics Korea University Seoul 136-713 South Korea |
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| Seong-Deog Yang | |
| Department of Mathematics Korea University Seoul 136-713 South Korea |
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