Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Submanifolds in spacetime with an auxiliary unphysical extra dimension
  and four-dimensional open and closed FRW universes   The explicit coordinate transformations which show the equivalence between
the FRW metrics of four-dimensional open and closed universes and the metrics
induced on appropriate submanifolds in a five-dimensional pseudo-Euclidean
space-time are presented.

36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th