2013
DOI: 10.1007/s11512-012-0169-5
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Biharmonic PNMC submanifolds in spheres

Abstract: We obtain several rigidity results for biharmonic submanifolds in S n with parallel normalized mean curvature vector field. We classify biharmonic submanifolds in S n with parallel normalized mean curvature vector field and with at most two distinct principal curvatures. In particular, we determine all biharmonic surfaces with parallel normalized mean curvature vector field in S n .Then we investigate, for (not necessarily compact) proper biharmonic submanifolds in S n , their type in the sense of B-Y. Chen. W… Show more

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Cited by 57 publications
(49 citation statements)
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“…where p i , h i (i = 1, 2) are polynomials concerning function λ 1 and given by 4 1 + a 1 λ 2 1 + a 2 , h 2 = −54(n + 3)λ 3 1 + a 3 λ 1 , h 3 = 12(n − 4)λ 3 1 + a 4 λ 1 .…”
Section: Proof Of Theorem 11mentioning
confidence: 99%
“…where p i , h i (i = 1, 2) are polynomials concerning function λ 1 and given by 4 1 + a 1 λ 2 1 + a 2 , h 2 = −54(n + 3)λ 3 1 + a 3 λ 1 , h 3 = 12(n − 4)λ 3 1 + a 4 λ 1 .…”
Section: Proof Of Theorem 11mentioning
confidence: 99%
“…It is clear from the definition that any biharmonic submanifold is biconservative. Now we are ready to prove the following theorem which generalizes the corresponding results in the Riemannian case given in [2]. Proof.…”
Section: )mentioning
confidence: 60%
“…For classification of biharmonic submanifolds with parallel mean curvature vector and |A| 2 = constant in sphere see [BMO3].…”
Section: Space Form Of Constant Sectional Curvature C Is F -Biharmonimentioning
confidence: 99%
“…For some recent geometric study of general biharmonic maps see [BK], [BFO2], [BMO2], [MO], [NUG], [Ou1], [Ou4], [OL], [Oua] and the references therein. For some recent study of biharmonic submanifolds see [CI], [Ji2], [Ji3], [Di], [CMO1], [CMO2], [BMO1], [BMO3], [Ou3], [OT], [OW], [NU], [TO], * [CM], [AGR] and the references therein. For biharmonic conformal immersions and submersions see [Ou2], [Ou5], [BFO1], [LO], [WO] and the references therein.…”
mentioning
confidence: 99%