Gauss–Bonnet Theorems in the Lorentzian Heisenberg Group and the Lorentzian Group of Rigid Motions of the Minkowski Plane

• Main Authors: Sining Wei, Yong Wang
• Format: Article
• Language: English
• Published: MDPI AG 2021-01-01
• Series: Symmetry
• Subjects: Lorentzian Heisenberg group; Lorentzian group of rigid motions of the minkowski plane; Gauss-Bonnet theorem; sub-Lorentzian limit
• Online Access: https://www.mdpi.com/2073-8994/13/2/173

The aim of this paper was to obtain Gauss–Bonnet theorems on the Lorentzian Heisenberg group and the Lorentzian group of rigid motions of the Minkowski plane. At the same time, the sub-Lorentzian limits of Gaussian curvature for surfaces which are <inline-formula><math display="inline"><semantics><msup><mi>C</mi><mn>2</mn></msup></semantics></math></inline-formula>-smooth in the Lorentzian Heisenberg group away from characteristic points and signed geodesic curvature for curves which are <inline-formula><math display="inline"><semantics><msup><mi>C</mi><mn>2</mn></msup></semantics></math></inline-formula>-smooth on surfaces are studied. Using a similar method, we also studied the corresponding contents on Lorentzian group of rigid motions of the Minkowski plane.