Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extendability of parallel sections in vector bundles   We address the following question: Given a differentiable manifold $M$ what
are the open subsets $U$ of $M$ such that, for all vector bundles $E$ over $M$
and all linear connections $\nabla$ on $E$, any $\nabla$-parallel section in
$E$ defined on $U$ extends to a $\nabla$-parallel section in $E$ defined on
$M$?
  For simply connected manifolds $M$ (among others) we describe the entirety of
all such sets $U$ which are, in addition, the complement of a $C^1$ submanifold
(boundary allowed) of $M$; this delivers a partial positive answer to a problem
posed by Antonio J. Di Scala and Gianni Manno. Furthermore, in case $M$ is an
open submanifold of $\mathbb R^n$, $2 \leq n$, we prove that the complement of
$U$ in $M$, not required to be a submanifold now, can have arbitrarily large
$n$-dimensional Lebesgue measure.

30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin