Connes’ functional formula of the Riemannian distance is generalized to the Lorentzian case using the so-called Lorentzian distance, the d’Alembert operator and the causal functions of a globally hyperbolic spacetime. As a step of the presented machinery, a proof of the almosteverywhere smoothness of the Lorentzian distance considered as a function of one of the two arguments is given. Afterwar...

This research article attempts to investigate anti-invariant Lorentzian submersions and the Lagrangian (LLS) from concircular structure [in short (LCS) n ] manifolds onto semi-Riemannian with relevant non-trivial examples. It is shown that horizontal distributions of such are not integrable their fibers totally geodesic. As a result, they can be geodesic maps. Anti-invariant also explored for h...

I review some of my recent work on non-lorentzian geometry. the classification kinematical Lie algebras and their associated Klein geometries. then describe Cartan geometries modelled them characterisation in terms intrinsic torsion.

{We consider neural units whose response functions are Lorentzians rather than the usual sigmoids or steps. This consideration is justiied by the fact that neurons can be paired and that a suitable diierence of the sigmoids of the paired neurons can create a window response function. Lorentzians are special cases of such windows and we take advantage of their simplicity to generate polynomial e...

We present the construction of the partition function of 3-dimensional gravity in the Lorentzian regime as a state sum model over a triangulation. This generalize the work of Ponzano and Regge to the case of Lorentzian signature.