Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On f-biharmonic maps and f-biharmonic submanifolds   f-Biharmonic maps are the extrema of the f-bienergy functional. f-biharmonic
submanifolds are submanifolds whose defining isometric immersions are
f-biharmonic maps. In this paper, we prove that an f-biharmonic map from a
compact Riemannian manifold into a non-positively curved manifold with constant
f-bienergy density is a harmonic map; any f-biharmonic function on a compact
manifold is constant, and that the inversions about $S^m$ for $m\ge 3$ are
proper f-biharmonic conformal diffeomorphisms. We derive f-biharmonic
submanifolds equations and prove that a surface in a manifold $(N^n, h)$ is an
f-biharmonic surface if and only it can be biharmonically conformally immersed
into $(N^n,h)$. We also give a complete classification of f-biharmonic curves
in 3-dimensional Euclidean space. Many examples of proper f-biharmonic maps and
f-biharmonic surfaces and curves are given.

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The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex