Gauss–Bonnet theorems and the Lorentzian Heisenberg group

Abstract

In this paper, we compute sub-Riemannian limits of Gaussian curvature for a C2-smooth surface in theLorentzian Heisenberg group for the second Lorentzian metric and the third Lorentzian metric and signed geodesiccurvature for C2-smooth curves on surfaces. We get Gauss–Bonnet theorems in the Lorentzian Heisenberg group forthe second Lorentzian metric and the third Lorentzian metric