Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Metric connections in projective differential geometry   We search for Riemannian metrics whose Levi-Civita connection belongs to a
given projective class. Following Sinjukov and Mikes, we show that such metrics
correspond precisely to suitably positive solutions of a certain projectively
invariant finite-type linear system of partial differential equations.
Prolonging this system, we may reformulate these equations as defining
covariant constant sections of a certain vector bundle with connection. This
vector bundle and its connection are derived from the Cartan connection of the
underlying projective structure.

3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
28
The categories of this paper are: alg-geom