Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane

DOI10.1007/S11425-019-1667-5zbMath1484.53094arXiv1912.00302OpenAlexW3016492212MaRDI QIDQ2238498

Yong Wang, Sining Wei

Publication date: 1 November 2021

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.00302

zbMATH Keywords

Gauss-Bonnet theoremGaussian curvatureaffine grouphorizontal mean curvaturesub-Riemannian limit(signed) geodesic curvaturegroup of rigid motions of Minkowski plane

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Global submanifolds (53C40) Sub-Riemannian geometry (53C17)

Related Items (9)

Gauss-Bonnet theorem in lorentzian Sasakian space forms ⋮ Sub-Lorentzian geometry of curves and surfaces in a Lorentzian Lie group ⋮ Affine Ricci solitons associated to the Bott connection on three-dimensional Lorentzian Lie groups ⋮ Gauss-Bonnet theorem in the universal covering group of Euclidean motion group \(E(2)\) with the general left-invariant metric ⋮ Gauss-Bonnet theorems for surfaces in sub-Riemannian three-dimensional manifolds ⋮ Affine generalized Ricci solitons of three-dimensional Lorentzian Lie groups associated to Yano connection ⋮ Generalized Ricci solitons of three-dimensional Lorentzian Lie groups associated canonical connections and Kobayashi-nomizu connections ⋮ The sub-Riemannian limit of curvatures for curves and surfaces and a Gauss-Bonnet theorem in the rototranslation group ⋮ 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

Cites Work

• Gauss-Bonnet theorem in sub-Riemannian Heisenberg space \(\mathbb H^1\)
• An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
• Correction to: ``Intrinsic curvature of curves and surfaces and a Gauss-Bonnet theorem in the Heisenberg group
• Intrinsic curvature of curves and surfaces and a Gauss-Bonnet theorem in the Heisenberg group

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