与自对偶爱因斯坦ACH度量相关的CR 3-流形的环境度量与庞加莱度量
Ambient and Poincaré metrics for CR $3$-manifolds associated with the self-dual Einstein ACH metric
- The University of Electro-Communications（电气通信大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文从自对偶爱因斯坦ACH度量出发，为3维CR流形的Fefferman共形流形构造了新的环境与庞加莱度量，其满足无穷阶爱因斯坦-麦克斯韦型方程，可用于构造CR不变算子，还实现了3维所有阶CR GJMS算子的环境度量构造。
AI中文摘要：
我们从相关的自对偶爱因斯坦ACH度量出发，为3维CR流形上的Fefferman共形流形构造了新的环境度量与庞加莱度量。与复Monge-Ampère方程近似解得到的经典环境度量和庞加莱度量不同，这些度量满足无穷阶的爱因斯坦-麦克斯韦型方程，而非里奇平坦或爱因斯坦方程。由于这些度量可被确定到无穷阶且无歧义，它们使我们能够构造涉及Tanaka-Webster曲率和挠率任意高阶导数的CR不变微分算子与局部CR不变量。作为应用，我们在3维情形下得到了所有阶CR GJMS（Gover-Graham）算子的环境度量构造。
英文摘要：
We construct new ambient and Poincaré metrics for the Fefferman conformal manifold over $3$-dimensional CR manifolds, starting from the associated self-dual Einstein ACH metric. Unlike the classical ambient and Poincaré metrics arising from approximate solutions to the complex Monge-Ampère equation, these metrics satisfy Einstein-Maxwell-type equations to infinite order rather than the Ricci-flat or Einstein equations. Since these metrics are determined to infinite order without ambiguity, they enable us to construct CR invariant differential operators and local CR invariants involving arbitrarily high order derivatives of the Tanaka-Webster curvature and torsion. As an application, we obtain the ambient metric construction of the CR GJMS (Gover-Graham) operators of all orders in dimension $3$.
