Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry

Andreas Bernig*, Dmitry Faifman, Gil Solanes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 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.

Original languageEnglish
Pages (from-to)11819-11848
Number of pages30
JournalJournal of Geometric Analysis
Volume31
Issue number12
DOIs
StatePublished - Dec 2021

Funding

FundersFunder number
Natural Sciences and Engineering Research Council of Canada
Deutsche ForschungsgemeinschaftBE 2484/5-2
Ministerio de Ciencia e InnovaciónPGC2018-095998-B-I00
European Regional Development Fund

    Keywords

    • Curvature measure
    • Lipschitz–Killing measures
    • Pseudo-Riemannian manifolds
    • Valuation
    • Weyl principle

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