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Herranz, F.J. Lucas Veguillas, Javier de Tobolski, M. 2018-12-27T16:33:08Z 2018-12-27T16:33:08Z 2017 Journal of Physics A: Mathematical and Theoretical, vol. 50 (2017) 495201 http://uvadoc.uva.es/handle/10324/33637 495201 A Lie–Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a t-dependent vector field taking values in a finite-dimensional Lie algebra, a Vessiot–Guldberg Lie algebra, of Hamiltonian vector fields relative to a Poisson structure. Its general solution can be written as an autonomous function, the superposition rule, of a generic finite family of particular solutions and a set of constants. We pioneer the study of Lie–Hamilton systems on Riemannian spaces (sphere, Euclidean and hyperbolic plane), pseudo-Riemannian spaces (anti-de Sitter, de Sitter, and Minkowski spacetimes) as well as on semi-Riemannian spaces (Newtonian spacetimes). Their corresponding constants of motion and superposition rules are obtained explicitly in a geometric way. This work extends the (graded) contraction of Lie algebras to a contraction procedure for Lie algebras of vector fields, Hamiltonian functions, and related symplectic structures, invariants, and superposition rules. eng info:eu-repo/semantics/openAccess Lie–Hamilton systems on curved spaces: A geometrical approach info:eu-repo/semantics/article