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Partner symmetries, group foliation and ASD Ricci-flat metrics without Killing vectors | | M. B. Sheftel
; A. A. Malykh
; | | Date: |
13 Jun 2013 | | Abstract: | We demonstrate how a combination of our recently developed methods of partner
symmetries, symmetry reduction in group parameters and a new version of the
group foliation method can produce noninvariant solutions of complex
Monge-Amp’ere equation (CMA) and provide a lift from invariant solutions of
CMA satisfying Boyer-Finley equation to non-invariant ones. Applying these
methods, we obtain a new noninvariant solution of CMA and the corresponding
Ricci-flat anti-self-dual Einstein-K"ahler metric with Euclidean signature
without Killing vectors, together with Riemannian curvature two-forms. There
are no singularities of the metric and curvature in a bounded domain if we
avoid very special choices of arbitrary functions of a single variable in our
solution. This metric does not describe gravitational instantons because the
curvature is not concentrated in a bounded domain. | | Source: | arXiv, 1306.3195 | | Services: | Forum | Review | PDF | Favorites | |
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