Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Biharmonic maps and morphisms from conformal mappings   Inspired by the all-important conformal invariance of harmonic maps on
two-dimensional domains, this article studies the relationship between
biharmonicity and conformality. We first give a characterization of biharmonic
morphisms, analogues of harmonic morphisms investigated by Fuglede and
Ishihara, which, in particular, explicits the conditions required for a
conformal map in dimension four to preserve biharmonicity and helps producing
the first example of a biharmonic morphism which is not a special type of
harmonic morphism. Then, we compute the bitension field of horizontally weakly
conformal maps, which include conformal mappings. This leads to several
examples of proper (i.e. non-harmonic) biharmonic conformal maps, in which
dimension four plays a pivotal role. We also construct a family of Riemannian
submersions which are proper biharmonic maps.

29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg