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

DOI10.1155/2021/1431082zbMath1477.53051OpenAlexW3189508400WikidataQ114070130 ScholiaQ114070130MaRDI QIDQ1981830

Jianyun Guan, Haiming Liu

Publication date: 7 September 2021

Published in: Journal of Function Spaces (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2021/1431082

zbMATH Keywords

Gauss-Bonnet theoremgeometries of Thurston

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Surfaces in Euclidean and related spaces (53A05) Curves in Euclidean and related spaces (53A04) Non-Euclidean differential geometry (53A35) Sub-Riemannian geometry (53C17)

Related Items (3)

Sub-Lorentzian geometry of curves and surfaces in a Lorentzian Lie group ⋮ Gauss-Bonnet theorem in the universal covering group of Euclidean motion group \(E(2)\) with the general left-invariant metric ⋮ Evolutoids of the mixed-type curves

Cites Work

• An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
• Classifying 3 and 4 dimensional homogeneous Riemannian manifolds by Cartan triples
• 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

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