Sub-Lorentzian geometry of curves and surfaces in a Lorentzian Lie group

DOI10.1155/2022/5396981zbMath1500.53040OpenAlexW4281814770WikidataQ115243478 ScholiaQ115243478MaRDI QIDQ2166660

Haiming Liu, Jianyun Guan

Publication date: 24 August 2022

Published in: Advances in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2022/5396981

zbMATH Keywords

generalized Gauss-Bonnet theoremsLorentzian approximantsRiemannian approximants

Mathematics Subject Classification ID

Local differential geometry of Lorentz metrics, indefinite metrics (53B30) Sub-Riemannian geometry (53C17)

Related Items (1)

Killing vectors and magnetic curves associated to Bott connection in Heisenberg group

Cites Work

• An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
• Left-invariant Lorentz metrics on Lie groups
• Classifying 3 and 4 dimensional homogeneous Riemannian manifolds by Cartan triples
• The sub-Riemannian limit of curvatures for curves and surfaces and a Gauss-Bonnet theorem in the group of rigid motions of Minkowski plane with general left-invariant metric
• Gauss-Bonnet theorem in lorentzian Sasakian space forms
• Correction to: ``Intrinsic curvature of curves and surfaces and a Gauss-Bonnet theorem in the Heisenberg group
• Gauss-Bonnet theorems in the BCV spaces and the twisted Heisenberg group
• The sub-Riemannian limit of curvatures for curves and surfaces and a Gauss-Bonnet theorem in the rototranslation group
• Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane
• Parallel surfaces in the motion groups \(E(1,1)\) and \(E(2)\)
• Intrinsic curvature of curves and surfaces and a Gauss-Bonnet theorem in the Heisenberg group
• A complete classification of parallel surfaces in three-dimensional homogeneous spaces
• Gauss-Bonnet theorem in the universal covering group of Euclidean motion group \(E(2)\) with the general left-invariant metric
• Gauss–Bonnet theorems and the Lorentzian Heisenberg group
• Lorentz Ricci solitons on 3-dimensional Lie groups

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