Jacobi fields and linear connections for arbitrary second-order ODEs.

DOI10.1016/S0393-0440(02)00030-XzbMath1039.53041OpenAlexW2022859893MaRDI QIDQ1864913

Yanyan Li

Publication date: 23 March 2003

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0393-0440(02)00030-x

zbMATH Keywords

second-order differential equationRaychaudhuri's equationJacobi tensors

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Dynamics induced by flows and semiflows (37C10) Geodesics in global differential geometry (53C22) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45)

Related Items (12)

An EDS approach to the inverse problem in the calculus of variations ⋮ Symmetries of second order differential equations on Lie algebroids ⋮ An intrinsic and exterior form of the Bianchi identities ⋮ Symmetries of Hamiltonian systems on Lie algebroids ⋮ Helmholtz conditions and symmetries for the time dependent case of the inverse problem of the calculus of variations ⋮ \(k\)-parameter geodesic variations ⋮ Lepage forms, closed 2-forms and second-order ordinary differential equations ⋮ A COMPLETE LIFT FOR SEMISPRAYS ⋮ The inverse problem in the calculus of variations: new developments ⋮ Linear connections and shape maps for second order ODEs with and without constraints ⋮ New progress in the inverse problem in the calculus of variations ⋮ Geometrization of the Leading Term in Acoustic Gaussian Beams

Cites Work

• Projective differential geometry and geodesic conservation laws in general relativity. I: Projective actions
• Projective differential geometry and geodesic conservation laws in general relativity. II: Conservation laws
• The geodesic spray, the vertical projection, and Raychaudhuri's equation
• A general Raychaudhuri's equation for second-order differential equations
• Derivations of forms along a map: The framework for time-dependent second-order equations
• Adjoint symmetries for time-dependent second-order equations
• A geometrical version of the Helmholtz conditions in time-dependent Lagrangian dynamics
• A complete classification of dynamical symmetries in classical mechanics
• A complete set of Bianchi identities for tensor fields along the tangent bundle projection
• The Large Scale Structure of Space-Time
• General Relativity
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