1. Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry
- Author
-
Dmitry Faifman, Andreas Bernig, and Gil Solanes
- Subjects
Mathematics - Differential Geometry ,Pure mathematics ,Riemannian geometry ,Characterization (mathematics) ,Space (mathematics) ,Curvature ,01 natural sciences ,symbols.namesake ,53C65, 53C50 ,0103 physical sciences ,FOS: Mathematics ,Uniqueness ,0101 mathematics ,Invariant (mathematics) ,ddc:510 ,Mathematics ,msc:53C65 ,010102 general mathematics ,Isotropy ,Differential geometry ,Differential Geometry (math.DG) ,msc:53C50 ,symbols ,010307 mathematical physics ,Geometry and Topology ,Mathematics::Differential Geometry - 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., Comment: 25 pages
- Published
- 2021