Abstract
Connes' noncommutative Riemannian distance formula is constructed in two steps, the first one being the construction of a pathindependent 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 pathindependent Lorentzian distance function.
Original language  English 

Pages (fromto)  111 
Number of pages  11 
Journal  Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 
Volume  6 
Issue number  064 
DOIs  
Publication status  Published  17 Aug 2010 
Keywords
 Noncommutative Geometry; Lorentzian distance; eikonal inequality
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Student Theses

Lorentzian approach to noncommutative geometry
Author: Franco, N., 31 Aug 2011Supervisor: Lambert, D. (Supervisor), Lemaitre, A. (Supervisor), Fuzfa, A. (Jury), Carletti, T. (President), MARTINETTI, P. (External person) (Jury) & LACHIEZEREY, M. (External person) (Jury)
Student thesis: Doc types › Doctor of Sciences
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