Seminar talk, 4 November 2020

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Speaker: Mikhail Sheftel

Title: Nonlocal symmetry of CMA generates ASD Ricci-flat metric with no Killing vectors

Abstract:
The complex Monge-Ampère equation (CMA) in a two-component form is treated as a bi-Hamiltonian system. I present explicitly the first nonlocal symmetry flow in each of the two hierarchies of this system. An invariant solution of CM A with respect to these nonlocal symmetries is constructed which, being a noninvariant solution in the usual sense, does not undergo symmetry reduction in the number of independent variables. I also construct the corresponding 4-dimensional anti-self-dual (ASD) Ricci-flat metric with either Euclidean or neutral signature. It admits no Killing vectors which is one of characteristic features of the famous gravitational instanton K3.

Language: English

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