Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry

Connes' noncommutative Riemannian distance formula is constructed in two steps, the first one being the construction of a path-independent geometrical functional using a global constraint on continuous functions. This paper generalizes this first step to Lorentzian geometry. We show that, in a...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2010
Main Author: Franco, N.
Format: Article
Language:English
Published: Інститут математики НАН України 2010
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/146501
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry / N. Franco // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 15 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Franco, N.
author_facet Franco, N.
citation_txt Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry / N. Franco // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 15 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description Connes' noncommutative Riemannian distance formula is constructed in two steps, the first one being the construction of a path-independent geometrical functional using a global constraint on continuous functions. This paper generalizes this first step to Lorentzian geometry. We show that, in a globally hyperbolic spacetime, a single global timelike eikonal condition is sufficient to construct a path-independent Lorentzian distance function.
first_indexed 2025-12-07T17:17:38Z
format Article
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id nasplib_isofts_kiev_ua-123456789-146501
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T17:17:38Z
publishDate 2010
publisher Інститут математики НАН України
record_format dspace
spelling Franco, N.
2019-02-09T19:27:42Z
2019-02-09T19:27:42Z
2010
Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry / N. Franco // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 15 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 58B34; 53C50
DOI:10.3842/SIGMA.2010.064
https://nasplib.isofts.kiev.ua/handle/123456789/146501
Connes' noncommutative Riemannian distance formula is constructed in two steps, the first one being the construction of a path-independent geometrical functional using a global constraint on continuous functions. This paper generalizes this first step to Lorentzian geometry. We show that, in a globally hyperbolic spacetime, a single global timelike eikonal condition is sufficient to construct a path-independent Lorentzian distance function.
This paper is a contribution to the Special Issue “Noncommutative Spaces and Fields”. The full collection is available at http://www.emis.de/journals/SIGMA/noncommutative.html.
 We would like to thank the anonymous referees for their useful remarks and relevant contribution to this paper.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry
Article
published earlier
spellingShingle Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry
Franco, N.
title Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry
title_full Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry
title_fullStr Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry
title_full_unstemmed Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry
title_short Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry
title_sort global eikonal condition for lorentzian distance function in noncommutative geometry
url https://nasplib.isofts.kiev.ua/handle/123456789/146501
work_keys_str_mv AT francon globaleikonalconditionforlorentziandistancefunctioninnoncommutativegeometry