This paper is concerned with deformations of Kundt metrics in the direction of type $III$ tensors and nil-Killing vector fields whose flows give rise to such deformations. We find various characterizations within the Kundt class in terms of nil-Killing vector fields and obtain a theorem classifying algebraic stability of tensors, which has an application in finding sufficient criteria for a type $III$ deformation of the metric to preserve spi's. This is used in order to specify Lie algebras of nil-Killing vector fields that preserve the spi's, for degenerate Kundt metrics. Using this we discuss the characterization of Kundt-CSI spacetimes in terms of nil-Killing vector fields.

中文翻译：

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Nil-Killing 矢量场和 III 型变形

本文关注的是昆特度量在类型 $III$ 张量和 nil-Killing 向量场方向上的变形，其流动会引起这种变形。我们在 Kundt 类中根据 nil-Killing 向量场找到了各种特征，并获得了分类张量代数稳定性的定理，这在找到度量的 $III$ 型变形的足够标准以保留 spi 时具有应用。这用于为退化的 Kundt 度量指定保留 spi 的 nil-Killing 向量场的李代数。使用这个，我们讨论了 Kundt-CSI 时空在 nil-Killing 向量场方面的表征。