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Lift of Invariant to Non-Invariant Solutions of Complex Monge-Amp'ere Equations | M. B. Sheftel
; A. A. Malykh
; | Date: |
11 Feb 2008 | Abstract: | 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. | Source: | arXiv, 0802.1463 | Services: | Forum | Review | PDF | Favorites |
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