Seminar talk, 4 November 2020: Difference between revisions
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| speaker = Mikhail Sheftel | | speaker = Mikhail Sheftel | ||
| title = Nonlocal symmetry of CMA generates ASD Ricci-flat metric with no Killing vectors | | 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 | | 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 CMA 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 | Language: English | ||
| video = | | video = https://video.gdeq.org/GDEq-zoom-seminar-20201104-Mikhail_Sheftel.mp4 | ||
| slides = | | slides = | ||
| references = | | references = {{arXiv|2007.08424}} | ||
| 79YY-MM-DD = 7979-88-95 | | 79YY-MM-DD = 7979-88-95 | ||
}} | }} | ||
Latest revision as of 08:40, 4 January 2025
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 CMA 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
Video
References:
arXiv:2007.08424