Projective collineations of decomposable spacetimes generated by the Lie point symmetries of geodesic equations

Abstract

We investigate the relation of the Lie point symmetries for the geodesic equations with the collineations of decomposable spacetimes. We review previous results in the literature on the Lie point symmetries of the geodesic equations and we follow a previous proposed geometric construction approach for the symmetries of differential equations. In this study we prove that the projective collineations of a $\left(n+1\right)$% -dimensional decomposable Riemannian space are the Lie point symmetries for geodesic equations of the $n$-dimensional subspace. We demonstrate the application of our results with the presentation of applications.

26 pages, to appear in Symmetry

References in corpus (5)

• Lie and Noether symmetries of geodesic equations and collineations
• Quadratic first integrals of autonomous conservative dynamical systems
• First integrals of holonomic systems without Noether symmetries
• Linearization from complex Lie point transformations
• Bianchi IX cosmologies in the Einstein-Skyrme system in a sector with non-trivial topological charge

Cited by in corpus (2)

• Hidden symmetries from distortions of the conformal structure
• The Equivalence Principle is NOT a Noether Symmetry