Gauss-Bonnet theorems and the Lorentzian Heisenberg group

Authors: Tong Wu, SINING WEI, YONG WANG

Abstract: In this paper, we compute sub-Riemannian limits of Gaussian curvature for a C$^{2}$-smooth surface in the Lorentzian Heisenberg group for the second Lorentzian metric and the third Lorentzian metric and signed geodesic curvature for C$^{2}$-smooth curves on surfaces. We get Gauss-Bonnet theorems in the Lorentzian Heisenberg group for the second Lorentzian metric and the third Lorentzian metric.

Keywords: Lorentzian Heisenberg group, the second Lorentzian metric, the third Lorentzian metric, Gauss-Bonnet theorem, sub-Riemannian limit

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