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Gauss–Bonnet Theorems for Lorentzian and Spacelike Surfaces Associated to Canonical Connections in the Lorentzian Heisenberg Group
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Gauss–Bonnet Theorems for Lorentzian and Spacelike Surfaces Associated to Canonical Connections in the Lorentzian Heisenberg Group
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Journal Article
Gauss–Bonnet Theorems for Lorentzian and Spacelike Surfaces Associated to Canonical Connections in the Lorentzian Heisenberg Group
2023
Overview
Canonical connections play important roles in studying the differential geometry properties of submanifolds in Lie groups. We define the first kind of canonical connection and the second canonical connection on Lorentzian approximations of the Heisenberg group. Moreover, we give the definitions of intrinsic curvature of a regular curve as well of intrinsic geodesic curvature of regular curves on Lorentzian and spacelike surfaces and of intrinsic Gaussian curvature of Lorentzian and spacelike surfaces away from characteristic points. Furthermore, we derive the expressions of those curvatures and prove Gauss–Bonnet Theorems for the Lorentzian and spacelike surfaces associated to canonical connections in the Lorentzian Heisenberg group.
Publisher
Pleiades Publishing,Springer Nature B.V
