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Some classifications
of biharmonic hypersurfaces with constant scalar
curvature
Shun Maeta and Ye-Lin Ou |
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Vol. 306 (2020), No. 1, 281–290
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Abstract |
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We give some classifications of biharmonic hypersurfaces with constant scalar curvature. These include biharmonic Einstein hypersurfaces in space forms, compact biharmonic hypersurfaces with constant scalar curvature in a sphere, and some complete biharmonic hypersurfaces of constant scalar curvature in space forms and in a nonpositively curved Einstein space. Our results provide additional cases (Theorem 2.3 and Proposition 2.8) that support the conjecture that a biharmonic submanifold in has constant mean curvature, and two more cases that support Chen’s conjecture on biharmonic hypersurfaces (Corollaries 2.2 and 2.7). |
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Keywords
biharmonic hypersurfaces, Einstein manifolds, constant
scalar curvature, constant mean curvature
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Mathematical Subject Classification 2010
Primary: 58E20
Secondary: 53C12
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Milestones
Received: 4 November 2018
Revised: 8 September 2019
Accepted: 12 December 2019
Published: 14 June 2020
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Authors |
| Shun Maeta | |
| Department of Mathematics Shimane University Matsue Japan |
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| Ye-Lin Ou | |
| Department of Mathematics Texas A & M University Commerce, TX United States |
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