Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrable Systems of Partial Differential Equations Determined by
  Structure Equations and Lax pair   It is shown how a system of evolution equations can be developed both from
the structure equations of a submanifold embedded in three-space as well as
from a matrix SO(6) Lax pair. The two systems obtained this way correspond
exactly when a constraint equation is selected and imposed on the system of
equations. This allows the coefficients of the second fundamental form to be
selected in a more general way so they need not be constants.

12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th