2010
DOI: 10.1002/mana.200710176
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Biharmonic hypersurfaces in 4‐dimensional space forms

Abstract: We investigate proper biharmonic hypersurfaces with at most three distinct principal curvatures in space forms. We obtain the full classification of proper biharmonic hypersurfaces in 4-dimensional space forms

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Cited by 87 publications
(72 citation statements)
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References 14 publications
(20 reference statements)
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“…Biharmonic submanifolds have been studied by many geometers. For example, see [2], [3], [7], [8], [11], [12], [13], [14], [15], [18], [20], [21], [22], and the references therein. In a different setting, in [9], Chen defined a biharmonic submanifold M ⊂ E n of the Euclidean space as its mean curvature vector field H satisfies ∆H = 0 , where ∆ is the Laplacian.…”
Section: Let (M G) and (N H) Be 2 Riemannian Manifolds And F : (M mentioning
confidence: 99%
“…Biharmonic submanifolds have been studied by many geometers. For example, see [2], [3], [7], [8], [11], [12], [13], [14], [15], [18], [20], [21], [22], and the references therein. In a different setting, in [9], Chen defined a biharmonic submanifold M ⊂ E n of the Euclidean space as its mean curvature vector field H satisfies ∆H = 0 , where ∆ is the Laplacian.…”
Section: Let (M G) and (N H) Be 2 Riemannian Manifolds And F : (M mentioning
confidence: 99%
“…Then, using certain results on isoparametric hypersurfaces, it was proved that there exist no compact properbiharmonic hypersurfaces of constant mean curvature and with three distinct principal curvatures everywhere in the unit Euclidean sphere (see [9]). …”
Section: Theorem ([8]) a Hypersurface With At Most Two Distinct Prinmentioning
confidence: 99%
“…(b) Any biharmonic hypersurfaces in H 4 (−1) is minimal (cf. [4]). (c) Any weakly convex biharmonic hypersurfaces in space form N m+1 (c) with c ≤ 0 is minimal (cf.…”
Section: Introductionmentioning
confidence: 99%