Partner Symmetries, Group Foliation and ASD Ricci-Flat Metrics without Killing Vectors

• Опубліковано в: : Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2013
• Автори: Sheftel, M.B., Malykh, A.A.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут математики НАН України 2013
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/149367
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Partner Symmetries, Group Foliation and ASD Ricci-Flat Metrics without Killing Vectors / M.B. Sheftel, A.A. Malykh // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 28 назв. — англ.

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-Ampère 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-Kähler 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.