Biharmonic submanifolds of $${\mathbb{C}P^n}$$
By D. Fetcu, Eric Loubeau, Stefano Montaldo, C. Oniciuc. 2009
66 citations recorded by the source corpus.
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 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.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/89e279726347404a0e49ea72f4b751abf13079bd
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Citations in the corpus
- Biharmonic hypersurfaces in Riemannian manifolds (2009, background): “mal. Based on these, Caddeo, Montaldo and Oniciuc [ 6 ] extended Chen’s conjecture to be the generalized Chen’s conjecture: any biharmonic submanifold in (N,h) with Riem N ≤ 0 is minimal.”
- Biharmonic hypersurfaces in 4‐dimensional space forms (2007, background): “Then, in [ 2 ] it was proved that the only proper biharmonic hypersphere S m (a), a ∈ (0,1), in S m+1 is S m ( 1”
- Classification results for biharmonic submanifolds in spheres (2007, methodology): “The attempt of classifying the biharmonic submanifolds in space forms was initiated in [7] and [ 2 ] with the following characterization results, obtained by splitting the bitension field in its normal and tangent components.”