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Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry
Symmetry, integrability and geometry: methods and applications, Tome 6 (2010) Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     author = {Nicolas Franco},
     title = {Global {Eikonal} {Condition} for {Lorentzian} {Distance} {Function} in {Noncommutative} {Geometry}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a63/}
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Nicolas Franco. Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry. Symmetry, integrability and geometry: methods and applications, Tome 6 (2010). http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a63/

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