论文标题
CMA的非局部对称性产生ASD RICCI-FLAT度量，没有杀伤向量
Nonlocal symmetry of CMA generates ASD Ricci-flat metric with no Killing vectors
论文作者
论文摘要
两种组成形式的复杂的Monge-ampère方程$（CMA）$被视为双汉米尔顿系统。我明确介绍了该系统两个层次结构中的每个层次中的第一个非局部对称流。 $ cma $相对于这些非本地对称性的不变解决方案是构建的，在通常的意义上，它是一种无创的解决方案，不会对自变量的数量进行对称减少。我还构建了具有欧几里得或中性签名的相应的4维反二维（ASD）RICCI-FLAT度量。它不承认杀死向量，这是著名的引力instanton $ k3 $的特征之一。对于具有欧几里得签名的度量，与重力激体相关，我明确计算了Levi-Civita连接1形和Riemann曲率张量。
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 $K3$. For the metric with the Euclidean signature, relevant for gravitational instantons, I explicitly calculate the Levi-Civita connection 1-forms and the Riemann curvature tensor.
