The geodesic spray, the vertical projection, and Raychaudhuri's equation

DOI10.1007/BF00767860zbMath0541.53012OpenAlexW1985515795MaRDI QIDQ794279

Mike Crampin, Geoff Prince

Publication date: 1984

Published in: General Relativity and Gravitation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00767860

zbMATH Keywords

Lie derivativespace-timegeodesic sprayRaychaudhuri's equationhorizontal subspace

Mathematics Subject Classification ID

Gravitational energy and conservation laws; groups of motions (83C40) Applications of local differential geometry to the sciences (53B50) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (7)

CR-structures and Lorentzian geometry ⋮ \(k\)-parameter geodesic variations ⋮ Shape maps for second order partial differential equations ⋮ Derivations of differential forms along the tangent bundle projection. II ⋮ Projective differential geometry and geodesic conservation laws in general relativity. II: Conservation laws ⋮ A general Raychaudhuri's equation for second-order differential equations ⋮ Jacobi fields and linear connections for arbitrary second-order ODEs.

Cites Work

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• Projective differential geometry and geodesic conservation laws in general relativity. II: Conservation laws
• Tangent bundle geometry Lagrangian dynamics
• On Horizontal Distributions on the Tangent Bundle of a Differentiable Manifold
• The Large Scale Structure of Space-Time

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