Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyperbolicity of holomorphic foliations with parabolic leaves   In this paper, we study a notion of hyperbolicity for hyperbolicity
foliations with 1-dimensional parabolic leaves, namely the non-existence of
holomorphic cylinders along the foliation - holomorphic maps from $\D^{n-1}
\times \C$ to the manifold sending each $\{*\} \times \C$ to a leaf. We
construct a tensor, that is a leaf-wise holomorphic section of a bundle above
the foliated manifold, which vanishes on an open saturated set if and only if
there exists such a cylinder through each point of this open set. Thanks to
this study, we prove that open sets saturated by compact leaves are union of
holomorphic cylinders along the foliation. We also give some more specific
results and examples in the case of a compact manifold, and of foliations with
one compact leaf or without any compact leaves.

24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph