2021
DOI: 10.3390/sym13061018
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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 n+1-dimensional decomposable Riemannian space are the Lie point symmetries for geodesic equations of the n-… Show more

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Cited by 4 publications
(2 citation statements)
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“…It is well known that, for the geodesic systems of equations, at least in the context of Riemannian geometry, the integrals of motion are closely related to the symmetries of the background manifold. For works regarding the symmetries of the geodesic equations as well as their geometrical significance, see [9][10][11][12][13][14][15][16][17].…”
Section: Introductionmentioning
confidence: 99%
“…It is well known that, for the geodesic systems of equations, at least in the context of Riemannian geometry, the integrals of motion are closely related to the symmetries of the background manifold. For works regarding the symmetries of the geodesic equations as well as their geometrical significance, see [9][10][11][12][13][14][15][16][17].…”
Section: Introductionmentioning
confidence: 99%
“…In [21] , a new λ -symmetry linearization criteria was established for second-order differential equations. In recent years, much attention has been done to the λ -symmetry linearization for solving nonlinear equations [22] , [23] . The analytical study is extended to include three conditions at which the cantilever beam is subjected to prior to the flexural motion.…”
Section: Introductionmentioning
confidence: 99%