Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Principal bundle structures among second order frame bundles   Using a model for the bundle $\hat{\mathcal F}^2M$ of semi-holonomic second
order frames of a manifold $M$ as an extension of the bundle ${\mathcal F}^2M$
of holonomic second order frames of $M$, we introduce in $\hat{\mathcal F}^2M$
a principal bundle structure over ${\mathcal F}^2M$, the structure group being
the additive group $A_2(n)$ of skew-symmetric bilinear maps from ${\Bbb R}^2
\times {\Bbb R}^n$ into ${\Bbb R}^n$. The composition of the projection of that
structure with the existing projection of the bundle $\tilde{\mathcal F}^2M$ of
non-holonomic second order frames of $M$ over $\hat{\mathcal F}^2M$ provides a
principal bundle structure in $\tilde{\mathcal F}^2M$ over ${\mathcal F}^2M$.
These results close an existing gap in the theory of second order frame
bundles.

3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th