The recently introduced Lipschitz–Killing curvature measures on pseudo-Riemannian manifolds satisfy a Weyl principle, i.e. are invariant under isometric embeddings. We show that they are uniquely characterized by this property. We apply this characterization to prove a Künneth-type formula for Lipschitz–Killing curvature measures, and to classify the invariant generalized valuations and curvature measures on all isotropic pseudo-Riemannian space forms.

中文翻译：

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伪黎曼几何中曲率测度的唯一性

最近引入的关于伪黎曼流形的 Lipschitz-Killing 曲率测量满足 Weyl 原理，即在等距嵌入下是不变的。我们表明，它们具有这种特性的独特特征。我们应用这种表征来证明 Lipschitz-Killing 曲率测度的 Künneth 型公式，并对所有各向同性伪黎曼空间形式的不变广义估值和曲率测度进行分类。