Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normal and tangent maps to frontals   The notion of frontals in Euclidean space is introduced and the normal and
tangent maps to frontals are studied for both geometrical and dynamical aspects
of frontals. Moreover we observe that parallels of the tangent map to a frontal
curve is right equivalent to the tangent map of a frontal curve under some
natural conditions.

32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol