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Symmetry, Integrability and Geometry: Methods and Applications, 2010, Volume 6, 064, 11 pp.
DOI: https://doi.org/10.3842/SIGMA.2010.064 (Mi sigma521) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry

Nicolas Franco

GAMASCO, Department of Mathematics, University of Namur FUNDP, 8 Rempart de la Vierge, B-5000 Namur, Belgium
Full-text PDF (199 kB) Citations (13)
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DOI: https://doi.org/10.3842/SIGMA.2010.064
Abstract: 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.
Keywords: noncommutative geometry; Lorentzian distance; eikonal inequality.
Received: March 30, 2010; in final form August 6, 2010; Published online August 17, 2010
Bibliographic databases:
Document Type: Article
MSC: 58B34; 53C50
Language: English
Citation: Nicolas Franco, “Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry”, SIGMA, 6 (2010), 064, 11 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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