Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Intrinsic geometry of oriented congruences in three dimensions   Starting from the classical notion of an oriented congruence (i.e. a
foliation by oriented curves) in $R^3$, we abstract the notion of an oriented
congruence structure. This is a 3-dimensional CR manifold $(M,H, J)$ with a
preferred splitting of the tangent space $TM=V\oplus H$. We find all local
invariants of such structures using Cartan's equivalence method refining
Cartan's classification of 3-dimensional CR structures. We use these invariants
and perform Fefferman like constructions, to obtain interesting Lorentzian
metrics in four dimensions, which include explicit Ricci-flat and Einstein
metrics, as well as not conformally Einstein Bach-flat metrics.

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The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
1
The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: econ
8
The categories of this paper are: hep-ex