Partner symmetries of the complex Monge-Ampere equation yield hyper-Kahler metrics without continuous symmetries

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dc.creatorMalykh, A. A.
dc.creatorNutku, Y.
dc.creatorSheftel, M. B.
dc.date2003-05-18
dc.date2003-07-25
dc.date.accessioned2026-07-07T10:50:35Z
dc.date.available2026-07-07T10:50:35Z
dc.descriptionWe extend the Mason-Newman Lax pair for the elliptic complex Monge-Ampère equation so that this equation itself emerges as an algebraic consequence. We regard the function in the extended Lax equations as a complex potential. We identify the real and imaginary parts of the potential, which we call partner symmetries, with the translational and dilatational symmetry characteristics respectively. Then we choose the dilatational symmetry characteristic as the new unknown replacing the Kähler potential which directly leads to a Legendre transformation and to a set of linear equations satisfied by a single real potential. This enables us to construct non-invariant solutions of the Legendre transform of the complex Monge-Ampère equation and obtain hyper-Kähler metrics with anti-self-dual Riemann curvature 2-form that admit no Killing vectors.
dc.descriptionsubmitted to J. Phys. A
dc.identifierhttps://arxiv.org/abs/math-ph/0305037
dc.identifierhttp://arxiv.org/abs/math-ph/0305037
dc.identifierJ.Phys.A36:10023-10038,2003
dc.identifierdoi:10.1088/0305-4470/36/39/304
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/184582
dc.subjectMathematical Physics
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.subjectDifferential Geometry
dc.subjectExactly Solvable and Integrable Systems
dc.subject35Q75, 83C15
dc.titlePartner symmetries of the complex Monge-Ampere equation yield hyper-Kahler metrics without continuous symmetries
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