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A novel exactly solvable Schr\"odinger equation with a position-dependentmass (PDM) describing a Coulomb problem in $D$ dimensions is obtained byextending the known duality relating the quantum $d$-dimensional oscillator and$D$-dimensional Coulomb problems in Euclidean spaces for $D = (d+2)/2$. As anintermediate step, a mapping between a quantum $d$-dimensional nonlinearoscillator of Mathews-Lakshmanan type (or oscillator in a space of constantcurvature) and a quantum $D$-dimensional Coulomb-like problem in a space ofnonconstant curvature is derived. It is finally reinterpreted in a PDMbackground.

Novel exactly solvable Schr\"odinger equations with a position-dependent mass in multidimensional spaces obtained from duality