Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry

  • 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.
Metadaten
Author:Andreas Bernig, Dmitry Faifman, Gil Solanes
URN:urn:nbn:de:hebis:30:3-636109
DOI:https://doi.org/10.1007/s12220-021-00702-4
ISSN:1559-002X
Parent Title (English):The journal of geometric analysis
Publisher:Springer
Place of publication:New York, NY
Document Type:Article
Language:English
Date of Publication (online):2021/06/14
Date of first Publication:2021/06/14
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2022/06/01
Tag:Curvature measure; Lipschitz–Killing measures; Pseudo-Riemannian manifolds; Valuation; Weyl principle
Volume:31
Issue:12
Page Number:30
First Page:11819
Last Page:11848
Note:
A.B. was supported by DFG grant BE 2484/5-2. D.F. was partially supported by an NSERC Discovery Grant. G.S. was supported by FEDER/MICINN grant PGC2018-095998-B-I00 and the Serra Húnter Programme. Open Access funding enabled and organized by Projekt DEAL.
HeBIS-PPN:496067974
Institutes:Informatik und Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:53-XX DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx) / 53Cxx Global differential geometry [See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx] / 53C50 Lorentz manifolds, manifolds with indefinite metrics
53-XX DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx) / 53Cxx Global differential geometry [See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx] / 53C65 Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx]
Sammlungen:Universitätspublikationen
Licence (German):License LogoCreative Commons - Namensnennung 4.0

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