单侧D型里奇平坦多中心度量
One-sided type-D Ricci-flat multi-centre metrics
AI总结：
本文基于LeBrun–Tod ansatz的Tod ansatz简化形式构造单侧D型里奇平坦多中心度量，系统研究其结构并结合多孤子解方案得出相关孤子数结论，推测结论对一般中心数成立。
AI中文摘要：
我们采用基于LeBrun–Tod ansatz构建的Tod ansatz简化形式，构造单侧D型里奇平坦多中心度量。这些度量是埃尔米特非凯勒且共形凯勒的，由一对生成势决定：辅助三维平坦空间中的轴对称调和函数（不同于Tod最初提出的那个）及其调和共轭。我们对这些多中心度量进行系统研究，包括其杆结构、渐近结构以及从中恢复各种已知闭式示例。特别地，我们证明，当将这些度量纳入本文作者用逆散射方法构造的平坦空间多孤子解方案时，中心数n≤3的这些度量，其自由孤子数比幻影孤子数大2或3；我们推测该结论对一般n也成立。
英文摘要：
We employ a simplified form of Tod's ansatz---which is built on the LeBrun--Tod ansatz---to construct one-sided type-D Ricci-flat multi-centre metrics. These metrics are Hermitian non-K{ä}hler and conformally K{ä}hler, and they are determined by a pair of generating potentials: an axisymmetric harmonic function (different from the one originally proposed by Tod) in an auxiliary 3D flat space and its harmonic conjugate. We carry out a systematic study of these multi-centre metrics, including their rod structure, asymptotic structure and recovering from them various known closed-form examples. In particular, we show that, when fitted into the scheme of multi-soliton solutions on flat space constructed by the present author using the inverse-scattering method, these metrics, with number of centres $n\le 3$, have a free-soliton number 2 or 3 greater than their phantom-soliton number; we conjecture that this is true for general $n$.
