Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diffeomorphisms preserving R-circles in three dimensional CR manifolds   R-circles in general three dimensional CR manifolds (of contact type) are the
analogues to traces of Lagrangian totally geodesic planes on the sphere viewed
as the boundary of two dimensional complex hyperbolic space. They form a family
of certain legendrian curves on the manifold. We prove that a diffeomorphism
between three dimensional CR manifolds which preserve circles is either a CR
diffeomorphism or conjugate CR diffeomorphism.

20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin