Approximate Lie symmetry conditions of autoparallels and geodesics

DOI10.1155/2020/8814657zbMath1474.34254OpenAlexW3097204072MaRDI QIDQ2657239

Sameerah Jamal

Publication date: 12 March 2021

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2020/8814657

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Invariance and symmetry properties for PDEs on manifolds (58J70)

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Cites Work

• The geometric nature of Lie and Noether symmetries
• Lie symmetries of geodesic equations and projective collineations
• Projective differential geometry and geodesic conservation laws in general relativity. I: Projective actions
• Approximate symmetries and conservation laws of the geodesic equations for the Schwarzschild metric
• \(n^{\text{th}}\)-order approximate Lagrangians induced by perturbative geometries
• Perturbative manifolds and the Noether generators of \(n\)th-order Poisson equations
• Approximate Noether symmetries and collineations for regular perturbative Lagrangians
• Quadratic conservation laws and collineations: a discussion
• Approximate conditions admitted by classes of the Lagrangian \(\mathcal{L} = \frac{1}{2}(- u^{\prime 2} + u^2) + \epsilon^i g_i(u, u^\prime, u)\)
• The connection between isometries and symmetries of geodesic equations of the underlying spaces
• On approximate symmetry and approximate solutions of the nonlinear wave equation with a small parameter
• Geodesic first integrals with explicit path-parameter dependence in Riemannian space–times
• Projective transformations and symmetries of differential equation
• APPROXIMATE SYMMETRIES

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