Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane
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Publication:2238498
DOI10.1007/S11425-019-1667-5zbMath1484.53094arXiv1912.00302OpenAlexW3016492212MaRDI QIDQ2238498
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
Gauss-Bonnet theoremGaussian curvatureaffine grouphorizontal mean curvaturesub-Riemannian limit(signed) geodesic curvaturegroup of rigid motions of Minkowski plane
Differential geometry of homogeneous manifolds (53C30) Global submanifolds (53C40) Sub-Riemannian geometry (53C17)
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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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