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Willmore
hypersurfaces with two distinct principal curvatures in
ℝn+1
Tongzhu Li |
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Vol. 256 (2012), No. 1, 129–149
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Abstract |
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We classify Willmore hypersurfaces of dimension n ≥ 3 in ℝn+1 with two distinct principal curvatures under Möbius transformation group of ℝn+1. We also characterize conformally flat Willmore hypersurfaces in ℝn+1 for n ≥ 4 in terms of the hyperelastic curves in two-dimensional real space forms. |
Keywords
Willmore hypersurfaces, conformally flat hypersurfaces,
elastic curve
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Mathematical Subject Classification 2010
Primary: 51B10, 53A30
Secondary: 53A55, 53B25, 53B50
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Milestones
Received: 7 March 2011
Accepted: 20 June 2011
Published: 6 May 2012
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Authors |
| Tongzhu Li | |
| Department of Mathematics Beijing Institute of Technology Beijing 100081 China |
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