Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Willmore surfaces in spheres via loop groups IV: on totally isotropic
  Willmore two-spheres in $S^6$   Totally isotropic surfaces in $S^6$ are not necessarily Willmore surfaces.
Therefore it is the first goal of this paper to derive a geometric
characterization of totally isotropic Willmore two-spheres in $S^6$. This will
naturally yield to a description of such surfaces in terms of the loop group
language. Moreover, applying the loop group method, we also obtain an algorithm
to construct totally isotropic Willmore two-spheres in $S^6$. As an
application, a new, totally isotropic Willmore two-sphere which is not
S-Willmore (i.e., has no dual surface) in $S^6$ is constructed, illustrating
the theory of this paper.

3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn