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.
|Number of pages||30|
|Journal||Journal of Geometric Analysis|
|Publication status||Published - Dec 2021|
- Curvature measure
- Lipschitz–Killing measures
- Pseudo-Riemannian manifolds
- Weyl principle