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A general approach is presented for quantizing a metric nonlinear system on amanifold of constant curvature. It makes use of a curvature dependent procedurewhich relies on determining Noether symmetries from the metric. The curvatureof the space functions as a constant parameter. For a specific metric whichdefines the manifold, Lie differentiation of the metric gives these symmetries.A metric is used such that the resulting Schrodinger equation can be solved interms of hypergeometric functions. This permits the investigation of both theenergy spectrum and wave functions exactly for this system.

Motion on Constant Curvature Spaces and Quantization Using Noether Symmetries