2009
DOI: 10.1007/s00209-009-0582-z
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Biharmonic submanifolds of $${\mathbb{C}P^n}$$

Abstract: We 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 submanifoldM in CP n and the bitension field of the inclusion of the corresponding Hopf-tube in S 2n+1 . Using this relation we produce new families of proper-biharmonic submanifold… Show more

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Cited by 44 publications
(26 citation statements)
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“…Results on proper-biharmonic submanifolds of a complex space form and, in particular, of the complex projective space were also proved (see [28]). There was obtained the relation between the bitension field of the inclusion ȷ : M → CP n of a submanifold in CP n and the bitension field of the inclusion ȷ : M → S 2n+1 of the corresponding Hopf cylinder in S 2n+1 ,…”
Section: Conjecture ([8]) Any Proper-biharmonic Submanifold In S N Hmentioning
confidence: 99%
“…Results on proper-biharmonic submanifolds of a complex space form and, in particular, of the complex projective space were also proved (see [28]). There was obtained the relation between the bitension field of the inclusion ȷ : M → CP n of a submanifold in CP n and the bitension field of the inclusion ȷ : M → S 2n+1 of the corresponding Hopf cylinder in S 2n+1 ,…”
Section: Conjecture ([8]) Any Proper-biharmonic Submanifold In S N Hmentioning
confidence: 99%
“…There exist many non-minimal biharmonic submanifolds in a sphere or a complex projective space (see, for example, [5] and [25]). On the other hand, the following conjecture proposed by Chen [12] is still open.…”
Section: Ideal Cr Immersions As Critical Points Of λ-Bienergy Functionalmentioning
confidence: 99%
“…[2]∼ [12], [15], [17], [18], [19], [22], [24], [32], etc...). Interestingly, their examples and classification results suggest that "any biharmonic submanifold in spheres has constant mean curvature".…”
Section: Introductionmentioning
confidence: 99%