Non-Hermitian Supersymmetric Factorization of Harmonic and Kepler-Coulomb Potentials in N-Dimensional Spaces of Constant Curvature

We propose a non-Hermitian supersymmetric factorization applied to harmonic and Kepler-Coulomb potentials, enhanced with an inverse-square term, in N-dimensional spaces of constant curvature. Constructed from a flat conformal metric, the obtained Hamiltonians offer a unified framework to treat spherical, hyperbolic and Euclidean geometries. The specificity of the approach lies in the introduction of non-adjoint scaling operators, which allow a natural generalization of supersymmetry in a non-Hermitian context. Spectral analysis reveals the decisive influence of curvature: in the harmonic case, it modifies the structure and distribution of levels, while for the Kepler-Coulomb potential, a negative curvature tends to weaken the bound states while a positive curvature strengthens their confinement. These results illustrate the fundamental role of geometry in quantum dynamics on curved spaces.