Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distinguished curves and first integrals on Poincar\'e-Einstein and
  other conformally singular geometries   We treat the problem of defining, and characterising in a practical way, an
appropriate class of distinguished curves for Poincar\'e-Einstein manifolds,
and other conformally singular geometries. These "generalised geodesics" agree
with geodesics away from the conformal singularity set and are shown to satisfy
natural "boundary conditions" at points where they meet or cross the metric
singularity set. We also characterise when they coincide with conformal
circles. In the case of (Poincar\'e-)Einstein manifolds, we are able to provide
a very general theory of first integrals for these distinguished curves. As
well as the general procedure outlined, a specific example is given.

18
The categories of this paper are: econ
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an