Talk
Geometric structures on lightlike geodesics spaces
- Nicolas Stutz (Université de Strasbourg)
Abstract
In this talk we will consider lightlike geodesics in Lorentzian manifolds. We will focus on the model space of conformal Lorentzian geometry, namely the Einstein Universe. It is known that the space of these geodesics is a contact manifold. In dimension three we will describe this contact structure thanks to the Engel structure with a split carried by the space of pointed lightlike geodesics. We will also discuss the four-dimensional case. In this framework, we will present a way to see that the space of lightlike geodesics is equipped with a Lorentzian CR structure in addition of the contact structure.