Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry

Nicolas Franco

doi:10.3842/SIGMA.2010.064

Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry

Nicolas Franco

Faculte des sciences

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Résumé

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.

langue originale	Anglais
Pages (de - à)	1-11
Nombre de pages	11
journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	6
Numéro de publication	064
Les DOIs	https://doi.org/10.3842/SIGMA.2010.064
Etat de la publication	Publié - 17 août 2010

Accès au document

10.3842/SIGMA.2010.064

Sigma10-064

http://www.emis.de/journals/SIGMA/2010/064/

Lorentzian approach to noncommutative geometry
Franco, N. (Auteur)Lambert, D. (Promoteur), Lemaitre, A. (Promoteur), Fuzfa, A. (Jury), Carletti, T. (Président), MARTINETTI, P. (Jury) & LACHIEZE-REY, M. (Jury), 31 août 2011
Student thesis: Doc types › Docteur en Sciences

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title = "Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry",

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",

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AB - 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.

KW - Noncommutative Geometry; Lorentzian distance; eikonal inequality

U2 - 10.3842/SIGMA.2010.064

DO - 10.3842/SIGMA.2010.064

M3 - Article

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JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry

Résumé

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Lorentzian approach to noncommutative geometry

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