Crampin, M. Hidden symmetries and Killing tensors. (English) Zbl 0551.58019 Rep. Math. Phys. 20, 31-40 (1984). The author investigates a notion of Killing tensor on a manifold M and its relation to symmetries of Hamiltonian systems on \(T^*M\) and their constants of motion. It is a well-known fact that a Killing vector field lifted from M to \(T^*M\) generates a symmetry of a corresponding Hamiltonian system (”obvious” symmetry). Lifting of a Killing tensor field from M to \(T^*M\) gives a vector field on \(T^*M\) which also generates a symmetry, but this symmetry is ”hidden”, i.e. mixes up coordinates and momenta in a nontrivial way. Examples are given leading to well-known symmetries of some classical systems Reviewer: Yu.E.Gliklikh Cited in 2 ReviewsCited in 13 Documents MSC: 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics 70H05 Hamilton’s equations Keywords:Killing tensor; Hamiltonian system; symmetries × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Havas, P., J. Math. Phys., 16, 2476 (1975) · Zbl 0314.35022 [2] Woodhouse, N. M.J., Comm. Math. Phys., 44, 9 (1975) · Zbl 0309.58012 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.