Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Four-dimensional Einstein metrics from biconformal deformations   Biconformal deformations take place in the presence of a conformal foliation,
deforming by different factors tangent to and orthogonal to the foliation.
Four-manifolds endowed with a conformal foliation by surfaces present a natural
context to put into effect this process. We develop the tools to calculate the
transformation of the Ricci curvature under such deformations and apply our
method to construct Einstein $4$-manifolds. One particular family of examples
have ends that collapse asymptotically to ${\mathbb R}^2$.

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The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
3
The categories of this paper are: physics
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The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph