The drift method, introduced in [22], provides a new formulation of the Einstein constraint equations, either in vacuum or with matter fields. The natural of the geometry underlying this method compensates for its slightly greater analytic complexity over, say, the conformal or conformal thin sandwich methods. We review this theory here and apply it to the study of solutions of the constraint equations with non-constant mean curvature. We show that this method reproduces previously known existence results obtained by other methods, and does better in one important regard. Namely, it can be applied even when the underlying metric admits conformal Killing (but not true Killing) vector fields. We also prove that the absence of true Killing fields holds generically.

中文翻译：

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共形场和爱因斯坦约束方程解空间的结构

[ 22 ]中引入的漂移方法提供了爱因斯坦约束方程的新公式，无论是在真空中还是在物质场中。这种方法所基于的几何结构的自然特性弥补了它比保形或保形薄三明治方法稍大的分析复杂性。我们在此回顾这一理论，并将其应用于研究具有非常数平均曲率的约束方程的解。我们表明，这种方法重现了其他方法获得的先前已知的存在结果，并且在一个重要方面做得更好。即，即使基础度量允许共形 Killing（但不是真正的 Killing）矢量场，它也可以应用。我们还证明，不存在真正的杀戮场是普遍存在的。