Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Biharmonic submanifolds of $\mathbb{C}P^n$   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.

29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio