000109652 001__ 109652 000109652 005__ 20230519145523.0 000109652 0247_ $$2doi$$a10.1088/1751-8121/ac17a4 000109652 0248_ $$2sideral$$a127487 000109652 037__ $$aART-2021-127487 000109652 041__ $$aeng 000109652 100__ $$0(orcid)0000-0003-4480-6535$$aCariñena, J.F.$$uUniversidad de Zaragoza 000109652 245__ $$aSuperintegrability on the 3-dimensional spaces with curvature. Oscillator-related and Kepler-related systems on the Sphere $S^3$ and on the Hyperbolic space $H^3$ 000109652 260__ $$c2021 000109652 5060_ $$aAccess copy available to the general public$$fUnrestricted 000109652 5203_ $$aThe superintegrability of several Hamiltonian systems defined on three-dimensional configuration spaces of constant curvature is studied. We first analyze the properties of the Killing vector fields, Noether symmetries and Noether momenta. Then we study the superintegrability of the harmonic oscillator, the Smorodinsky-Winternitz system and the harmonic oscillator with ratio of frequencies 1:1:2 and additional nonlinear terms on the three-dimensional sphere S-3 (kappa > 0) and on the hyperbolic space H-3 (kappa < 0). In the second part we present a study first of the Kepler problem and then of the Kepler problem with additional nonlinear terms in these two curved spaces, S-3 (kappa > 0) and H-3 (kappa < 0). We prove their superintegrability and we obtain, in all the cases, the maximal number of functionally independent integrals of motion. All the mathematical expressions are presented using the curvature kappa as a parameter, in such a way that particularizing for kappa > 0, kappa = 0, or kappa < 0, the corresponding properties are obtained for the system on the sphere S-3, the Euclidean space E-3, or the hyperbolic space H-3, respectively. 000109652 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000109652 590__ $$a2.331$$b2021 000109652 592__ $$a0.76$$b2021 000109652 594__ $$a4.0$$b2021 000109652 591__ $$aPHYSICS, MATHEMATICAL$$b14 / 56 = 0.25$$c2021$$dQ1$$eT1 000109652 593__ $$aMathematical Physics$$c2021$$dQ1 000109652 591__ $$aPHYSICS, MULTIDISCIPLINARY$$b45 / 86 = 0.523$$c2021$$dQ3$$eT2 000109652 593__ $$aStatistics and Probability$$c2021$$dQ1 000109652 593__ $$aStatistical and Nonlinear Physics$$c2021$$dQ1 000109652 593__ $$aPhysics and Astronomy (miscellaneous)$$c2021$$dQ1 000109652 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/submittedVersion 000109652 700__ $$0(orcid)0000-0002-8402-2332$$aRañada, M.F.$$uUniversidad de Zaragoza 000109652 700__ $$aSantander M. 000109652 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica 000109652 773__ $$g54, 36 (2021), 365201 [27 pp.]$$pJournal of Physics A-Mathematical and Theoretical$$tJournal of Physics A-Mathematical and Theoretical$$x1751-8113 000109652 8564_ $$s461625$$uhttps://zaguan.unizar.es/record/109652/files/texto_completo.pdf$$yPreprint 000109652 8564_ $$s1523039$$uhttps://zaguan.unizar.es/record/109652/files/texto_completo.jpg?subformat=icon$$xicon$$yPreprint 000109652 909CO $$ooai:zaguan.unizar.es:109652$$particulos$$pdriver 000109652 951__ $$a2023-05-18-15:24:07 000109652 980__ $$aARTICLE