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.
Keywords
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}
}
Comments
25 pages