The Schouten curvature tensor and the Jacobi equation in sub-Riemannian geometry

DOI10.1007/s10958-021-05361-yzbMath1467.53034OpenAlexW3155126155WikidataQ115382159 ScholiaQ115382159MaRDI QIDQ2027329

V. R. Krym

Publication date: 26 May 2021

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-021-05361-y

zbMATH Keywords

Heisenberg groupJacobi equationhorizontal geodesicsnonholonomicity tensor

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Sub-Riemannian geometry (53C17)

Cites Work

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• Reduction of nonholonomic variation problems to isoperimetric ones and connections in principal bundles
• Nonholonomous geodesics as solutions to Euler-Lagrange integral equations and the differential of the exponential mapping
• Sub-Riemannian geometry
• Geodesic flow on SL(2,\({\mathbb{R}})\) with nonholonomic constraints
• Geodesic equations for a charged particle in the unified theory of gravitational and electromagnetic interactions
• The curvature tensor and the Einstein equations for a four-dimensional nonholonomic distribution
• Jacobi fields for a nonholonomic distribution
• Existence of abnormal minimizing geodesics in sub-Riemannian geometry
• A survey of singular curves in sub-Riemannian geometry
• Sub-Riemannian distance on the Lie group \(\mathrm{SL}(2)\)
• Nonholonomic Riemann and Weyl tensors for flag manifolds
• Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung
• Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics
• Book Review: A comprehensive introduction to sub-Riemannian geometry. From the Hamiltonian viewpoint