Timelike Hilbert and Funk geometries

TIMELIKE HILBERT AND FUNK GEOMETRIES

Athanase Papadopoulos (1, 2) , Sumio Yamada (3)

1 IRMA - Institut de Recherche Mathématique Avancée
2 TIFR - Tata Institute for Fundamental Research
3 Department of Mathematics [Gakushuin]

A timelike space is a Hausdorff topological space equipped with a partial order relation $<$ and a distance function $\rho$ satisfying a collection of axioms including a set of compatibility conditions between the partial order relation and the distance function. The distance function is defined only on a subset of the product of the space with itself that contains the diagonal, namely, $\rho(x,y)$ is defined if and only if $x

Mots clés: Busemann ge-ometry; metric geometry; convexity; timelike Hilbert geometry; Lorentzian; relativity.; light cone; Timelike space; Busemann geometry; geometry; relativity; AMS classification— 53C70; timelike Funk geometry; time inequality; Lorentzian geometry; relativity AMS classification-53C70; exterior convex geometry; Busemann geom- etry AMS classification-53C70; 53C22; 5C10; 53C23; 53C50; 53C45

Domaines: Topologie géométrique [math.GT]; Géométrie différentielle [math.DG]; Géométrie métrique [math.MG]

Athanase Papadopoulos, Sumio Yamada. TIMELIKE HILBERT AND FUNK GEOMETRIES. 2016. ⟨hal-01276762v5⟩