论文标题
自我偶发的爱因斯坦空间和一般的天上方程式。本征函数作为坐标
Self-dual Einstein spaces and the general heavenly equation. Eigenfunctions as coordinates
论文作者
论文摘要
表明本征构成了爱因斯坦空间的特权坐标，其基本的管理方程式被揭示为一般的天上方程式。这里开发的形式主义可用于从算法上链接各种已知的天堂方程。特别是，通过特征函数检索和解释了Plebanski的第一个和第二个天上方程之间的经典联系。此外，发现了与最近引入的TED方程的降低连接，该方程构成了4+4维的一般天堂方程。这些是通过（部分）Legendre转换获得的。作为一种特定的应用，我们证明，由兼容的无散布式海洛塔方程组管辖的大量自偶联的爱因斯坦空间确实是四维的，因为（仿制药）指标不承认任何（适当或非宣传）的同伴杀死载体。这概括了特定类别的自偶联的爱因斯坦空间与编码三维爱因斯坦 - 韦尔几何形状的无分散海景方程之间的已知联系。
Eigenfunctions are shown to constitute privileged coordinates of self-dual Einstein spaces with the underlying governing equation being revealed as the general heavenly equation. The formalism developed here may be used to link algorithmically a variety of known heavenly equations. In particular, the classical connection between Plebanski's first and second heavenly equations is retrieved and interpreted in terms of eigenfunctions. In addition, connections with travelling wave reductions of the recently introduced TED equation which constitutes a 4+4-dimensional integrable generalisation of the general heavenly equation are found. These are obtained by means of (partial) Legendre transformations. As a particular application, we prove that a large class of self-dual Einstein spaces governed by a compatible system of dispersionless Hirota equations is genuinely four-dimensional in that the (generic) metrics do not admit any (proper or non-proper) conformal Killing vectors. This generalises the known link between a particular class of self-dual Einstein spaces and the dispersionless Hirota equation encoding three-dimensional Einstein-Weyl geometries.
