Curvature collineations in general relativity. I

DOI10.1063/1.529075zbMath0745.53019OpenAlexW2088877901MaRDI QIDQ3987308

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Publication date: 28 June 1992

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.529075

zbMATH Keywords

curvature tensorcurvature collineationsspace timecurvature preserving transformationscurvature type

Mathematics Subject Classification ID

Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory (83C20) Applications of local differential geometry to the sciences (53B50) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (14)

Curvature collineations in general relativity. II ⋮ Some remarks on special conformal and special projective symmetries in general relativity ⋮ Ricci and matter collineations in space-time ⋮ Symmetries of Energy-Momentum Tensor: Some Basic Facts ⋮ Affine collineations in general relativity and their fixed point structure ⋮ TELEPARALLEL KILLING VECTORS OF THE EINSTEIN UNIVERSE ⋮ Pseudosymmetry collineations ⋮ Symmetries of Bianchi I space–times ⋮ Conformal Ricci collineations of space-times ⋮ Classification and conformal symmetry in three-dimensional space–times ⋮ Some remarks on symmetries and transformation groups in general relativity ⋮ Energy Conditions and Conservation Laws in LRS Bianchi Type I Spacetimes via Noether Symmetries ⋮ Curvature and Weyl collineations of Bianchi type V space-times ⋮ Positive energy condition and conservation laws in Kantowski-Sachs spacetime via Noether symmetries

Cites Work

• On local and global existence of Killing vector-fields
• Curvature collineations and the determination of the metric from the curvature in General Relativity
• Algebraic determination of the metric from the curvature in general relativity
• The uniqueness of \(g_{ij}\) in terms of \(R^l_{ijk}\)
• Local and global algebraic structures in general relativity
• Conformal symmetries and fixed points in space-time
• Invariant Formulation of Gravitational Radiation Theory
• Holonomy groups in general relativity
• Curvature of generic space-times in general relativity
• Curvature structure in general relativity
• Affine collineations in space-time
• The global extension of local symmetries in general relativity
• The Riemann tensor, the metric tensor, and curvature collineations in general relativity
• Curvature Collineations: A Fundamental Symmetry Property of the Space-Times of General Relativity Defined by the Vanishing Lie Derivative of the Riemann Curvature Tensor

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