On sub-Riemannian geodesic curvature in dimension three

DOI10.1515/acv-2020-0021zbMath1497.53070arXiv1910.13132OpenAlexW2982341876WikidataQ115237075 ScholiaQ115237075MaRDI QIDQ2156040

Mathieu Kohli, Davide Barilari

Publication date: 15 July 2022

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.13132

zbMATH Keywords

geodesic curvaturesub-Riemannian geometryregularity of the distance

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Sub-Riemannian geometry (53C17)

Cites Work

• Gauss-Bonnet theorem in sub-Riemannian Heisenberg space \(\mathbb H^1\)
• Sub-Riemannian structures on 3D Lie groups
• Sub-Riemannian curvature in contact geometry
• Differential forms on contact manifolds
• An application of the moving frame method to integral geometry in the Heisenberg group
• The differential geometry of curves in the Heisenberg groups
• Any sub-Riemannian metric has points of smoothness
• On the Dido problem and plane isoperimetric problems
• Small sub-Riemannian balls on \(\mathbf R^3\)
• Exponential mappings for contact sub-Riemannian structures
• A metric interpretation of the geodesic curvature in the Heisenberg group
• Intrinsic curvature of curves and surfaces and a Gauss-Bonnet theorem in the Heisenberg group
• Isoperimetric inequalities & volume comparison theorems on CR manifolds
• Variational Problems on Contact Riemannian Manifolds
• Curvature: A Variational Approach
• On Jacobi fields and a canonical connection in sub-Riemannian geometry

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