伙伴对称性、群叶化与无Killing向量的ASD Ricci-平坦图
Partner Symmetries, Group Foliation and ASD Ricci-Flat Metrics without Killing Vectors
摘要：
我们展示了如何结合我们最近开发的方法的合作伙伴对称性，对称性减少组参数和一个新版本的组叶状方法可以产生复杂的Monge-Ampère方程（CMA）的非不变的解决方案，并提供了一个电梯CMA满足Boyer-Finley方程的非不变的。应用这些方法，我们得到了CMA的一个新的非不变解和相应的Ricci平坦的反自对偶Einstein-Kähler度量，它具有不含Killing向量的Euclidean签名，以及黎曼曲率的两种形式.如果我们在解中避免选择非常特殊的单变量任意函数，则在有界区域中度量和曲率不存在奇异性。这个度量并不描述引力瞬子，因为曲率并不集中在有界区域。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
