Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flat surfaces along swallowtails   We consider developable surfaces along the singular set of a swallowtail
which are considered to be flat approximations of the swallowtail. For the
study of singularities of such developable surfaces, we introduce the notion of
Darboux frames along swallowtails and invariants. As a by-product, we give a
new example of a frontal which is locally homeomorphic to a swallowtail.

8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess