We study the Schrödinger equation for the isotropic oscillator in three-dimensional space with constant positive curvature. So, the description of solutions for the corresponding Schrödinger equation based on the spherical coordinates. By comparing the Schrödinger equation of harmonic oscillator in constant positive curvature to the associated Jacobi polynomial, we obtain the energy spectrum and wave function. The associated Jacobi equation help us to factorize the Schrödinger equation for the isotropic oscillator. The first order equation from factorization method lead us to define the raising and lowering operators. These operators are supersymmetric structure related to the Hamiltonian partner, thus we obtain the corresponding supercharges.
