Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Short Proof of the Pontryagin Maximum Principle on Manifolds   Applying the Tubular Neighborhood Theorem, we give a short and new proof of
the Pontryagin Maximum Principle on a smooth manifold. The idea is as follows.
Given a control system on a manifold $M$, we embed it into an open subset of
some $\mathbb R^n$, and extend the control system to the open set. Then, we
apply the Pontryagin Maximum Principle on $\mathbb R^n$ to the extended system
and project the consequence to $M$.

24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an