论文标题
4D中的二阶PDE，具有半翼保形结构
Second-order PDEs in 4D with half-flat conformal structure
论文作者
论文摘要
我们研究4D中的二阶PDE，其在每个溶液上由方程式的特征变化定义为半翼（自偶或反自我偶）的共形结构。我们证明这一要求意味着Monge-Ampere财产。由于保形结构的半片性等同于存在非平凡的宽松对的存在，因此我们的结果解释了以下观察结果：所有已知的二阶二阶可集成无分散PDE在尺寸四个及更高的Monge-Ampere类型中。还获得了一些具有半翼共形结构的4D的Monge-Ampere方程的部分分类结果。
We study second-order PDEs in 4D for which the conformal structure defined by the characteristic variety of the equation is half-flat (self-dual or anti-self-dual) on every solution. We prove that this requirement implies the Monge-Ampere property. Since half-flatness of the conformal structure is equivalent to the existence of a nontrivial dispersionless Lax pair, our result explains the observation that all known scalar second-order integrable dispersionless PDEs in dimensions four and higher are of Monge-Ampere type. Some partial classification results of Monge-Ampere equations in 4D with half-flat conformal structure are also obtained.
