Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry-Reference-Cited by-同舟云学术

Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry

Published:2021-06-14 Issue:12 Volume:31 Page:11819-11848
ISSN:1050-6926
Container-title:The Journal of Geometric Analysis
language:en
Short-container-title:J Geom Anal

Author:

Bernig Andreas^ORCID,Faifman Dmitry,Solanes Gil

Abstract

AbstractThe 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.

Funder

Deutsche Forschungsgemeinschaft

FEDER/MICINN

Serra Hunter Programme

Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada

Publisher

Springer Science and Business Media LLC

Subject

Geometry and Topology

Link

https://link.springer.com/content/pdf/10.1007/s12220-021-00702-4.pdf

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