Gauss—Bonnet Theorems in the Lorentzian Heisenberg Group and the Lorentzian Group of Rigid Motions of the Minkowski Plane
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 xmlns="http://ww...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-01-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/13/2/173 |
| Summary: | 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 xmlns="http://www.w3.org/1998/Math/MathML" 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 xmlns="http://www.w3.org/1998/Math/MathML" 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. |
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| ISSN: | 2073-8994 |