Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A generalized integrability problem for G-Structures   Given an $\widetilde n$-dimensional manifold $\widetilde M$ equipped with a
$\widetilde G$-structure $\widetilde\pi:\widetilde P\rightarrow \widetilde M$,
there is a naturally induced $G$-structure $\pi: P\rightarrow M$ on any
submanifold $M\subset\widetilde M$ that satisfies appropriate regularity
conditions. We study generalized integrability problems for a given
$G$-structure $\pi: P\rightarrow M$, namely the questions of whether it is
locally equivalent to induced $G$-structures on regular submanifolds of
homogeneous $\widetilde G$-structures $\widetilde\pi:\widetilde P\to
\widetilde{H}/\widetilde{K}$. If $\widetilde\pi:\widetilde P\to
\widetilde{H}/\widetilde{K}$ is flat $k$-reductive we introduce a sequence of
generalized curvatures taking values in appropriate cohomology groups and prove
that the vanishing of these curvatures are necessary and sufficient conditions
for the solution of the corresponding generalized integrability problems.

4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
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
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn