Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lift of Invariant to Non-Invariant Solutions of Complex Monge-Amp\`ere
  Equations   We show how partner symmetries of the elliptic and hyperbolic complex
Monge-Amp\`ere equations (CMA and HCMA) provide a lift of non-invariant
solutions of three- and two-dimensional reduced equations, i.e., a lift of
invariant solutions of the original CMA and HCMA equations, to non-invariant
solutions of the latter four-dimensional equations. The lift is applied to
non-invariant solutions of the two-dimensional Helmholtz equation to yield
non-invariant solutions of CMA, and to non-invariant solutions of
three-dimensional wave equation and three-dimensional hyperbolic Boyer-Finley
equation to yield non-invariant solutions of HCMA. By using these solutions as
metric potentials, it is possible to construct four-dimensional Ricci-flat
metrics of Euclidean and ultra-hyperbolic signatures that have non-zero
curvature tensors and no Killing vectors.

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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: acc-phys