LAUSR

Via coupling constant metamorphosis, we construct new families of superintegrable Hamiltonian systems that correspond to n dimensional extensions of the Tremblay–Turbiner–Winternitz and Post–Winternitz systems on curved spaces. These families confirm the conjecture stated in (Rodríguez and Tempesta 2022 J. Phys. A: Math. Theor. 55 50LT01) to be true, at least in some special cases. Their physical relevance lies in the fact that they can be related to monopole systems with non-radially symmetric potential. In this way we obtain new integrable and superintegrable monopole systems on curved spaces that, for special choice of the parameters, include Taub-NUT spaces.