Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new volume form on sub-Riemannian Heisenberg manifolds and their
  non-collapsed limits   In this paper, we introduce a new volume form to compute Riemannian and
sub-Riemannian metrics simultaneously. By considering a uniform lower bound of
the total measure induced from this volume, we show that the non-collapsed
limit of a sequence of compact Heisenberg manifolds is isometric to again a
compact Heisenberg manifold of the same dimension.

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The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin