Biharmonic submanifolds of $\mathbb{C}P^n$

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dc.creatorFetcu, D.
dc.creatorLoubeau, E.
dc.creatorMontaldo, S.
dc.creatorOniciuc, C.
dc.date2009-02-02
dc.date.accessioned2026-07-07T12:36:58Z
dc.date.available2026-07-07T12:36:58Z
dc.descriptionWe give some general results on proper-biharmonic submanifolds of a complex space form and, in particular, of the complex projective space. These results are mainly concerned with submanifolds with constant mean curvature or parallel mean curvature vector field. We find the relation between the bitension field of the inclusion of a submanifold $\bar{M}$ in $\mathbb{C}P^n$ and the bitension field of the inclusion of the corresponding Hopf-tube in $\mathbb{S}^{2n+1}$. Using this relation we produce new families of proper-biharmonic submanifolds of $\mathbb{C}P^n$. We study the geometry of biharmonic curves of $\mathbb{C}P^n$ and we characterize the proper-biharmonic curves in terms of their curvatures and complex torsions.
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/0902.0268
dc.identifierhttp://arxiv.org/abs/0902.0268
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/218281
dc.subjectDifferential Geometry
dc.subject58E20
dc.titleBiharmonic submanifolds of $\mathbb{C}P^n$
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