Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry
| Autor: | Dmitry Faifman, Andreas Bernig, Gil Solanes |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
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 |
| Popis: | 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 |
| Databáze: | OpenAIRE |
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