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Uniqueness of curvature measures in pseudo-Riemannian geometry

Differential Geometry 2022-09-14 v1

Abstract

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 K\"unneth-type formula for Lipschitz-Killing curvature measures, and to classify the invariant generalized valuations and curvature measures on all isotropic pseudo-Riemannian space forms.

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Cite

@article{arxiv.2009.02230,
  title  = {Uniqueness of curvature measures in pseudo-Riemannian geometry},
  author = {Andreas Bernig and Dmitry Faifman and Gil Solanes},
  journal= {arXiv preprint arXiv:2009.02230},
  year   = {2022}
}

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25 pages