Invariants and Infinitesimal Transformations for Contact Sub-Lorentzian Structures on 3-Dimensional Manifolds

In this article we develop some elementary aspects of a theory of symmetry in sub-Lorentzian geometry. First of all we construct invariants characterizing isometric classes of sub-Lorentzian contact 3 manifolds. Next we characterize vector fields which generate isometric and conformal symmetries in general sub-Lorentzian manifolds. We then focus attention back to the case where the underlying manifold is a contact 3 manifold and more specifically when the manifold is also a Lie group and the structure is left-invariant

Invariants of contact sub-pseudo-Riemannian structures and Einstein-Weyl geometry

We consider local geometry of sub-pseudo-Riemannian structures on contact manifolds. We construct fundamental invariants of the structures and show that the structures give rise to Einstein-Weyl geometries in dimension 3, provided that certain additional conditions are satisfied

3-dimensional left-invariant sub-Lorentzian contact structures

We provide a classification of ts-invariant sub-Lorentzian structures on 3 dimensional contact Lie groups. Our approach is based on invariants arising form the construction of a normal Cartan connection. \ua9 2016 Elsevier B.V