Calculus of Variations and Geometric Measure Theory

I. Markina - S. Wojtowytsch

On the Alexandrov Topology of sub-Lorentzian Manifolds

created by wojtowytsch on 13 Sep 2018



Inserted: 13 sep 2018

Year: 2013

ArXiv: 1301.0635 PDF


It is commonly known that in Riemannian and sub-Riemannian Geometry, the metric tensor on a manifold defines a distance function. In Lorentzian Geometry, instead of a distance function it provides causal relations and the Lorentzian time-separation function. Both lead to the definition of the Alexandrov topology, which is linked to the property of strong causality of a space-time. We studied three possible ways to define the Alexandrov topology on sub-Lorentzian manifolds, which usually give different topologies, but agree in the Lorentzian case. We investigated their relationships to each other and the manifold's original topology and their link to causality.