Gauss-Bonnet theorem in sub-Riemannian Heisenberg space \(\mathbb H^1\)
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Publication:334636
DOI10.1007/S10883-016-9338-3zbMath1362.53040arXiv1210.7110OpenAlexW1646697690WikidataQ115383664 ScholiaQ115383664MaRDI QIDQ334636
Marcos M. Diniz, Jose Miguel Martins Veloso
Publication date: 1 November 2016
Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1210.7110
Related Items (12)
Gauss-Bonnet theorems in the generalized affine group and the generalized BCV spaces ⋮ On sub-Riemannian geodesic curvature in dimension three ⋮ Rotation surfaces of constant Gaussian curvature and mean curvature in sub-Riemannian Heisenberg space \(\mathbb H^1\) ⋮ First variation of the Hausdorff measure of non-horizontal submanifolds in sub-Riemannian stratified Lie groups ⋮ Intrinsic curvature of curves and surfaces and a Gauss-Bonnet theorem in the Heisenberg group ⋮ Gauss–Bonnet theorems and the Lorentzian Heisenberg group ⋮ Gauss-Bonnet theorems for surfaces in sub-Riemannian three-dimensional manifolds ⋮ Intrinsic sub-Laplacian for hypersurface in a contact sub-Riemannian manifold ⋮ Gauss-Bonnet theorems in the BCV spaces and the twisted Heisenberg group ⋮ Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane ⋮ A metric interpretation of the geodesic curvature in the Heisenberg group ⋮ On the induced geometry on surfaces in 3D contact sub-Riemannian manifolds
Cites Work
- An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
- A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds
- Sub-Riemannian calculus on hypersurfaces in Carnot groups
- Intrinsic curvature of curves and surfaces and a Gauss-Bonnet theorem in the Heisenberg group
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